{"id":46,"date":"2018-07-20T11:44:34","date_gmt":"2018-07-20T09:44:34","guid":{"rendered":"http:\/\/mathquiz.fr\/?page_id=46"},"modified":"2018-07-25T20:24:10","modified_gmt":"2018-07-25T18:24:10","slug":"fonction-logarithme-neperien","status":"publish","type":"page","link":"https:\/\/mathquiz.fr\/?page_id=46","title":{"rendered":"Fonction logarithme n\u00e9perien"},"content":{"rendered":"<div id=\"mtq_quiz_area-1\" class=\"mtq_quiz_area mtq_color_blue\"> \r\n  <!--Quiz generated using mTouch Quiz Version 3.1.3 by G. Michael Guy (http:\/\/gmichaelguy.com\/quizplugin\/)-->\r\n        \r\n      \r\n  <!-- Shortcode entered mtouchquiz id=7 --> \r\n  <!-- Shortcode interpreted mtouchquiz id=7 alerts=on singlepage=on hints=off startscreen=on finalscreen=on multiplechances=off showanswers=now show_stamps=on randomq=on randoma=on status=on labels=on title=on proofread=off list=off time=off scoring=off formid= vform=on autoadvance=off autosubmit=off inform=off forcecf=off forcegf=off offset=1 questions=5 firstid=54 lastid=58 color=blue --> \r\n  <!--form action=\"\" method=\"post\" class=\"quiz-form\" id=\"quiz-7\"-->\r\n    <div id=\"mtq_quiztitle-1\" class=\"mtq_quiztitle\" >\r\n  <h2>Fonction logarithme n\u00e9perien<\/h2>\r\n  <\/div>\r\n      <noscript>\r\n  <div id=\"mtq_javawarning-1\" class=\"mtq_javawarning\">\r\n  Veuillez attendre la fin du chargement de l'activit\u00e9. <\/br>Si l'activit\u00e9 se ne charge pas, essayez de rafra\u00eechir votre navigateur. Cette page n\u00e9cessite aussi Javascript. Veuillez la visiter avec Javascript activ\u00e9.  <div class=\"mtq_failed_button\" onclick=\"mtq_start_one(1)\">\r\n  Si le chargement \u00e9choue, cliquez ici pour r\u00e9-essayer  <\/div><\/div>\r\n  <\/noscript>\r\n    <div id=\"mtq_instructions-1\" class=\"mtq_instructions\"><\/div> <div id=\"mtq_start_button-1\" class='mtq_action_button mtq_css_button mtq_start_button' onclick='mtq_start_quiz(1)'> <div class=\"mtq_start_text\">\r\n  D\u00e9part  <\/div> <\/div>\r\n  <div id=\"mtq_quiz_results_bubble-1\" class=\"mtq_quiz_results_bubble\"> <div id=\"mtq_quiz_results-1\" class=\"mtq_quiz_results\"><p>F\u00e9licitation - vous avez compl\u00e9t\u00e9 <em>Fonction logarithme n\u00e9perien<\/em>.<\/p><p>Vous avez obtenu  %%SCORE%% sur %%TOTAL%%.<\/p><p>Votre performance a \u00e9t\u00e9 \u00e9valu\u00e9e \u00e0 %%RATING%%<\/p> <br>    \r\n  <\/div> <div id=\"mtq_quiz_results_highlight-1\" class=\"mtq_quiz_results_highlight\">\r\n  Vos r\u00e9ponses sont surlign\u00e9es ci-dessous.  <\/div> <\/div>\r\n    \r\n  <!-- root element for mtqscrollable -->\r\n\r\n  <div id=\"mtq_question_container-1\" style='display:none'>\r\n  <div >\r\n          <div class='mtq_question mtq_scroll_item-1' id='mtq_question-1-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 1<\/div><div id='mtq_stamp-1-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-1-1' class='mtq_question_text'>R\u00e9soudre <span class=\"wp-katex-eq\" data-display=\"false\">ln(-2x-3)=ln(7x-1)<\/span><\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-1-1-1' onclick='mtq_button_click(1,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-1-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 1, Choice 1'>A<\/div><div id='mtq_marker-1-1-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-1-1-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">x=-\\dfrac{2}{9}<\/span> <\/div><\/td><\/tr><tr id='mtq_row-1-2-1' onclick='mtq_button_click(1,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-1-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 1, Choice 2'>B<\/div><div id='mtq_marker-1-2-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-1-2-1' class='mtq_answer_text'>Cette \u00e9quation n'admet pas de solution<\/div><\/td><\/tr><tr id='mtq_row-1-3-1' onclick='mtq_button_click(1,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-1-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 1, Choice 3'>C<\/div><div id='mtq_marker-1-3-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-1-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">x=2<\/span> <\/div><\/td><\/tr><tr id='mtq_row-1-4-1' onclick='mtq_button_click(1,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-1-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 1, Choice 4'>D<\/div><div id='mtq_marker-1-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-1-4-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">x=\\dfrac{7}{3}<\/span> <\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-1-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 1:&nbsp;<\/div><div class='mtq_explanation-text'> <span class=\"wp-katex-eq\" data-display=\"false\">ln(-2x-3)=ln(7x-1)<\/span> est \u00e9quivalent \u00e0 r\u00e9soudre <span class=\"wp-katex-eq\" data-display=\"false\">-2x-3=7x-1<\/span> \r\n\r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">-2x-7x=-1+3<\/span> \r\n\r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">-9x=2<\/span> \r\n\r\n\r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">x=-\\dfrac{2}{9}<\/span> \r\n\r\n<ol>\r\n<\/ol>\r\n\r\nOr <span class=\"wp-katex-eq\" data-display=\"false\">ln(-\\dfrac{2}{9})<\/span> n'existe pas. La fonction <span class=\"wp-katex-eq\" data-display=\"false\">ln(x)<\/span> est d\u00e9finie pour tout <span class=\"wp-katex-eq\" data-display=\"false\">x\\in\\mathbb{R}^+<\/span>. Comme cette solution n'est pas positive, l'\u00e9quation n'admet pas de solution.<\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-2-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 2<\/div><div id='mtq_stamp-2-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-2-1' class='mtq_question_text'>R\u00e9soudre <span class=\"wp-katex-eq\" data-display=\"false\">ln(2x+3)=ln(7x-1)<\/span><\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-2-1-1' onclick='mtq_button_click(2,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-2-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 2, Choice 1'>A<\/div><div id='mtq_marker-2-1-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-2-1-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">x=\\dfrac{2}{3}<\/span> <\/div><\/td><\/tr><tr id='mtq_row-2-2-1' onclick='mtq_button_click(2,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-2-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 2, Choice 2'>B<\/div><div id='mtq_marker-2-2-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-2-2-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">x=\\dfrac{4}{5}<\/span> <\/div><\/td><\/tr><tr id='mtq_row-2-3-1' onclick='mtq_button_click(2,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-2-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 2, Choice 3'>C<\/div><div id='mtq_marker-2-3-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-2-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">x=\\dfrac{2}{5}<\/span> <\/div><\/td><\/tr><tr id='mtq_row-2-4-1' onclick='mtq_button_click(2,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-2-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 2, Choice 4'>D<\/div><div id='mtq_marker-2-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-2-4-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">x=\\dfrac{5}{7}<\/span> <\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-2-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 2:&nbsp;<\/div><div class='mtq_explanation-text'> <span class=\"wp-katex-eq\" data-display=\"false\">ln(2x+3)=ln(7x-1)<\/span> est \u00e9quivalent \u00e0 r\u00e9soudre <span class=\"wp-katex-eq\" data-display=\"false\">2x+3=7x-1<\/span> \r\n\r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">2x-7x=-1-3<\/span> \r\n\r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">-5x=-4<\/span> \r\n\r\n\r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">x=\\dfrac{-4}{-5}<\/span> \r\n\r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">x=\\dfrac{4}{5}<\/span> <\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-3-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 3<\/div><div id='mtq_stamp-3-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-3-1' class='mtq_question_text'>Soit <span class=\"wp-katex-eq\" data-display=\"false\">(u_n)<\/span> une suite de la forme <span class=\"wp-katex-eq\" data-display=\"false\">u_{n}=300\\times 0,5^n +200<\/span>.\r\n\r\nD\u00e9terminer (par calcul) le plus petit entier <span class=\"wp-katex-eq\" data-display=\"false\">n<\/span> telle que <span class=\"wp-katex-eq\" data-display=\"false\">u_n\\leqslant 210<\/span><\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-3-1-1' onclick='mtq_button_click(3,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-3-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 3, Choice 1'>A<\/div><div id='mtq_marker-3-1-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-3-1-1' class='mtq_answer_text'>3<\/div><\/td><\/tr><tr id='mtq_row-3-2-1' onclick='mtq_button_click(3,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-3-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 3, Choice 2'>B<\/div><div id='mtq_marker-3-2-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-3-2-1' class='mtq_answer_text'>5<\/div><\/td><\/tr><tr id='mtq_row-3-3-1' onclick='mtq_button_click(3,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-3-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 3, Choice 3'>C<\/div><div id='mtq_marker-3-3-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-3-3-1' class='mtq_answer_text'>6<\/div><\/td><\/tr><tr id='mtq_row-3-4-1' onclick='mtq_button_click(3,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-3-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 3, Choice 4'>D<\/div><div id='mtq_marker-3-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-3-4-1' class='mtq_answer_text'>4<\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-3-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 3:&nbsp;<\/div><div class='mtq_explanation-text'> <span class=\"wp-katex-eq\" data-display=\"false\">u_n\\leqslant 210<\/span>\r\n\r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">300\\times 0,5^n +200\\leqslant 210<\/span>\r\n\r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">300\\times 0,5^n \\leqslant 210-200<\/span>\r\n\r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">300\\times 0,5^n \\leqslant 10<\/span>\r\n\r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\"> 0,5^n \\leqslant \\dfrac{10}{300}<\/span>\r\n\r\n\r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\"> 0,5^n \\leqslant \\dfrac{1}{30}<\/span>\r\n\r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\"> ln(0,5^n) \\leqslant ln(\\dfrac{1}{30})<\/span>\r\n\r\n\r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\"> nln(0,5) \\leqslant ln(\\dfrac{1}{30})<\/span> (cf propri\u00e9t\u00e9 4)\r\n\r\n\r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">n\\geqslant\\dfrac{ln(\\dfrac{1}{30})}{ln(0,5)}<\/span>\r\n\r\n<ol>\r\n<\/ol>\r\n\r\n(on a change le signe de l'in\u00e9galit\u00e9 car ln(0,5)<0)\r\n\r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\"> \\dfrac{ln(\\dfrac{1}{30})}{ln(0,5)}\\approx 4,9 <\/span>, par cons\u00e9quent le plus petit entier <span class=\"wp-katex-eq\" data-display=\"false\">n<\/span> telle que <span class=\"wp-katex-eq\" data-display=\"false\">u_n\\leqslant 210<\/span> est <span class=\"wp-katex-eq\" data-display=\"false\">n=5<\/span>.<\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-4-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 4<\/div><div id='mtq_stamp-4-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-4-1' class='mtq_question_text'>R\u00e9soudre <span class=\"wp-katex-eq\" data-display=\"false\">2^x=4<\/span><\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-4-1-1' onclick='mtq_button_click(4,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-4-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 4, Choice 1'>A<\/div><div id='mtq_marker-4-1-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-4-1-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">e^2<\/span><\/div><\/td><\/tr><tr id='mtq_row-4-2-1' onclick='mtq_button_click(4,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-4-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 4, Choice 2'>B<\/div><div id='mtq_marker-4-2-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-4-2-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">2<\/span><\/div><\/td><\/tr><tr id='mtq_row-4-3-1' onclick='mtq_button_click(4,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-4-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 4, Choice 3'>C<\/div><div id='mtq_marker-4-3-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-4-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">ln(2)<\/span><\/div><\/td><\/tr><tr id='mtq_row-4-4-1' onclick='mtq_button_click(4,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-4-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 4, Choice 4'>D<\/div><div id='mtq_marker-4-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-4-4-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">\\dfrac{e^2}{ln(2)}<\/span><\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-4-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 4:&nbsp;<\/div><div class='mtq_explanation-text'> <span class=\"wp-katex-eq\" data-display=\"false\">2^x=4<\/span>\r\n\r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">ln(2^x)=ln(4)<\/span>\r\n\r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">xln(2)=ln(4)<\/span>, (cf propri\u00e9t\u00e9 4)\r\n\r\n\r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">x=\\dfrac{ln(4)}{ln(2)}=\\dfrac{ln(2^2)}{ln(2)}=\\dfrac{2ln(2)}{ln(2)}=2<\/span><\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-5-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 5<\/div><div id='mtq_stamp-5-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-5-1' class='mtq_question_text'>R\u00e9soudre <span class=\"wp-katex-eq\" data-display=\"false\">x^{12}=7<\/span><\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-5-1-1' onclick='mtq_button_click(5,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-5-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 5, Choice 1'>A<\/div><div id='mtq_marker-5-1-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-5-1-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">x=\\dfrac{ln(7)}{12}<\/span> <\/div><\/td><\/tr><tr id='mtq_row-5-2-1' onclick='mtq_button_click(5,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-5-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 5, Choice 2'>B<\/div><div id='mtq_marker-5-2-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-5-2-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">x=\\dfrac{ln(7)}{12}<\/span> <\/div><\/td><\/tr><tr id='mtq_row-5-3-1' onclick='mtq_button_click(5,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-5-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 5, Choice 3'>C<\/div><div id='mtq_marker-5-3-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-5-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">x=e^{\\dfrac{ln(12)}{7}}<\/span> <\/div><\/td><\/tr><tr id='mtq_row-5-4-1' onclick='mtq_button_click(5,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-5-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 5, Choice 4'>D<\/div><div id='mtq_marker-5-4-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-5-4-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">x=e^{\\dfrac{ln(7)}{12}}<\/span> <\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-5-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 5:&nbsp;<\/div><div class='mtq_explanation-text'> (cf propri\u00e9t\u00e9 6, pour y r\u00e9pondre directement sinon \ud83d\ude42\r\n\r\n<ol>\r\n<\/oL>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">x^{12}=7<\/span> \r\n\r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">ln(x^{12})=ln(7)<\/span>\r\n\r\n<ol>\r\n<\/ol>\r\n\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">12ln(x)=ln(7)<\/span> (cf propri\u00e9t\u00e9 4)\r\n\r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">ln(x)=\\dfrac{ln(7)}{12}<\/span> \r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">e^{ln(x)}=e^{\\dfrac{ln(7)}{12}}<\/span> \r\n<ol>\r\n<\/ol>\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">x=e^{\\dfrac{ln(7)}{12}}<\/span> (cf propri\u00e9t\u00e9 2.3)\r\n<ol>\r\n<\/ol><\/div><\/div><\/div>            <div id=\"mtq_results_request-1\" class=\"mtq_results_request mtq_scroll_item-1\">\r\n        Une fois termin\u00e9, cliquez sur le bouton ci-dessous. Toutes les questions que vous n'avez pas compl\u00e9t\u00e9es sont marqu\u00e9es comme incorrectes.        <span id=\"mtq_results_button-1\" class='mtq_action_button mtq_css_button mtq_results_button'  onclick='mtq_get_results(1)'> <span class=\"mtq_results_text\">\r\n        Obtenir les r\u00e9sultats        <\/span> <\/span> <\/div>\r\n                <!--End of mtqscrollable items--> \r\n    \r\n  <\/div>\r\n  <!--End of mtqscrollable--> \r\n  <!--mtq_status-->\r\n    <div id=\"mtq_quiz_status-1\" class=\"mtq_quiz_status\">\r\n  Il y a 5 questions \u00e0 compl\u00e9ter.  <\/div>\r\n      <\/div> \r\n  <!--Holds all questions-->\r\n    <div id=\"mtq_variables\" class=\"mtq_preload\" style=\"display:none\"> <input type='hidden' id='mtq_id-1' name='mtq_id_value' value='1' \/><input type='hidden' name='question_id[]' value='57'\/><input type='hidden' id='mtq_is_answered-1-1' value='0'\/><input type='hidden' id='mtq_is_correct-1-1' value='0'\/><input type='hidden' id='mtq_is_worth-1-1' value='100'\/><input type='hidden' id='mtq_num_attempts-1-1' value='0'\/><input type='hidden' id='mtq_points_awarded-1-1' value='0'\/><input type='hidden' id='mtq_is_correct-1-1-1' value='0'\/><input type='hidden' id='mtq_was_selected-1-1-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-1-1-1' value='0'\/><input type='hidden' id='mtq_has_hint-1-1-1' value='0'\/><input type='hidden' id='mtq_is_correct-1-2-1' value='1'\/><input type='hidden' id='mtq_was_selected-1-2-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-1-2-1' value='0'\/><input type='hidden' id='mtq_has_hint-1-2-1' value='0'\/><input type='hidden' id='mtq_is_correct-1-3-1' value='0'\/><input type='hidden' id='mtq_was_selected-1-3-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-1-3-1' value='0'\/><input type='hidden' id='mtq_has_hint-1-3-1' value='0'\/><input type='hidden' id='mtq_is_correct-1-4-1' value='0'\/><input type='hidden' id='mtq_was_selected-1-4-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-1-4-1' value='0'\/><input type='hidden' id='mtq_has_hint-1-4-1' value='0'\/><input type='hidden' id='mtq_num_ans-1-1' value='4' \/><input type='hidden' id='mtq_num_correct-1-1' value='1' \/><input type='hidden' name='question_id[]' value='56'\/><input type='hidden' id='mtq_is_answered-2-1' value='0'\/><input type='hidden' id='mtq_is_correct-2-1' value='0'\/><input type='hidden' id='mtq_is_worth-2-1' value='100'\/><input type='hidden' id='mtq_num_attempts-2-1' value='0'\/><input type='hidden' id='mtq_points_awarded-2-1' value='0'\/><input type='hidden' id='mtq_is_correct-2-1-1' value='0'\/><input type='hidden' id='mtq_was_selected-2-1-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-2-1-1' value='0'\/><input type='hidden' id='mtq_has_hint-2-1-1' value='0'\/><input type='hidden' id='mtq_is_correct-2-2-1' value='1'\/><input type='hidden' id='mtq_was_selected-2-2-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-2-2-1' value='0'\/><input type='hidden' id='mtq_has_hint-2-2-1' value='0'\/><input type='hidden' id='mtq_is_correct-2-3-1' value='0'\/><input type='hidden' id='mtq_was_selected-2-3-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-2-3-1' value='0'\/><input type='hidden' id='mtq_has_hint-2-3-1' value='0'\/><input type='hidden' id='mtq_is_correct-2-4-1' value='0'\/><input type='hidden' id='mtq_was_selected-2-4-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-2-4-1' value='0'\/><input type='hidden' id='mtq_has_hint-2-4-1' value='0'\/><input type='hidden' id='mtq_num_ans-2-1' value='4' \/><input type='hidden' id='mtq_num_correct-2-1' value='1' \/><input type='hidden' name='question_id[]' value='55'\/><input type='hidden' id='mtq_is_answered-3-1' value='0'\/><input type='hidden' id='mtq_is_correct-3-1' value='0'\/><input type='hidden' id='mtq_is_worth-3-1' value='100'\/><input type='hidden' id='mtq_num_attempts-3-1' value='0'\/><input type='hidden' id='mtq_points_awarded-3-1' value='0'\/><input type='hidden' id='mtq_is_correct-3-1-1' value='0'\/><input type='hidden' id='mtq_was_selected-3-1-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-3-1-1' value='0'\/><input type='hidden' id='mtq_has_hint-3-1-1' value='0'\/><input type='hidden' id='mtq_is_correct-3-2-1' value='1'\/><input type='hidden' id='mtq_was_selected-3-2-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-3-2-1' value='0'\/><input type='hidden' id='mtq_has_hint-3-2-1' value='0'\/><input type='hidden' id='mtq_is_correct-3-3-1' value='0'\/><input type='hidden' id='mtq_was_selected-3-3-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-3-3-1' value='0'\/><input type='hidden' id='mtq_has_hint-3-3-1' value='0'\/><input type='hidden' id='mtq_is_correct-3-4-1' value='0'\/><input type='hidden' id='mtq_was_selected-3-4-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-3-4-1' value='0'\/><input type='hidden' id='mtq_has_hint-3-4-1' value='0'\/><input type='hidden' id='mtq_num_ans-3-1' value='4' \/><input type='hidden' id='mtq_num_correct-3-1' value='1' \/><input type='hidden' name='question_id[]' value='54'\/><input type='hidden' id='mtq_is_answered-4-1' value='0'\/><input type='hidden' id='mtq_is_correct-4-1' value='0'\/><input type='hidden' id='mtq_is_worth-4-1' value='100'\/><input type='hidden' id='mtq_num_attempts-4-1' value='0'\/><input type='hidden' id='mtq_points_awarded-4-1' value='0'\/><input type='hidden' id='mtq_is_correct-4-1-1' value='0'\/><input type='hidden' id='mtq_was_selected-4-1-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-4-1-1' value='0'\/><input type='hidden' id='mtq_has_hint-4-1-1' value='0'\/><input type='hidden' id='mtq_is_correct-4-2-1' value='1'\/><input type='hidden' id='mtq_was_selected-4-2-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-4-2-1' value='0'\/><input type='hidden' id='mtq_has_hint-4-2-1' value='0'\/><input type='hidden' id='mtq_is_correct-4-3-1' value='0'\/><input type='hidden' id='mtq_was_selected-4-3-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-4-3-1' value='0'\/><input type='hidden' id='mtq_has_hint-4-3-1' value='0'\/><input type='hidden' id='mtq_is_correct-4-4-1' value='0'\/><input type='hidden' id='mtq_was_selected-4-4-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-4-4-1' value='0'\/><input type='hidden' id='mtq_has_hint-4-4-1' value='0'\/><input type='hidden' id='mtq_num_ans-4-1' value='4' \/><input type='hidden' id='mtq_num_correct-4-1' value='1' \/><input type='hidden' name='question_id[]' value='58'\/><input type='hidden' id='mtq_is_answered-5-1' value='0'\/><input type='hidden' id='mtq_is_correct-5-1' value='0'\/><input type='hidden' id='mtq_is_worth-5-1' value='100'\/><input type='hidden' id='mtq_num_attempts-5-1' value='0'\/><input type='hidden' id='mtq_points_awarded-5-1' value='0'\/><input type='hidden' id='mtq_is_correct-5-1-1' value='0'\/><input type='hidden' id='mtq_was_selected-5-1-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-5-1-1' value='0'\/><input type='hidden' id='mtq_has_hint-5-1-1' value='0'\/><input type='hidden' id='mtq_is_correct-5-2-1' value='0'\/><input type='hidden' id='mtq_was_selected-5-2-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-5-2-1' value='0'\/><input type='hidden' id='mtq_has_hint-5-2-1' value='0'\/><input type='hidden' id='mtq_is_correct-5-3-1' value='0'\/><input type='hidden' id='mtq_was_selected-5-3-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-5-3-1' value='0'\/><input type='hidden' id='mtq_has_hint-5-3-1' value='0'\/><input type='hidden' id='mtq_is_correct-5-4-1' value='1'\/><input type='hidden' id='mtq_was_selected-5-4-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-5-4-1' value='0'\/><input type='hidden' id='mtq_has_hint-5-4-1' value='0'\/><input type='hidden' id='mtq_num_ans-5-1' value='4' \/><input type='hidden' id='mtq_num_correct-5-1' value='1' \/> <div id=\"mtq_have_completed_string\" class=\"mtq_preload\">\r\n    Vous avez compl\u00e9t\u00e9    <\/div> <div id=\"mtq_questions_string\" class=\"mtq_preload\">\r\n    questions    <\/div> <div id=\"mtq_question_string\" class=\"mtq_preload\">\r\n    question    <\/div> <div id=\"mtq_your_score_is_string\"  class=\"mtq_preload\">\r\n    Votre score est de    <\/div> <div id=\"mtq_correct_string\"  class=\"mtq_preload\">\r\n    Correct    <\/div> <div id=\"mtq_wrong_string\"  class=\"mtq_preload\">\r\n    Faux    <\/div> <div id=\"mtq_partial_string\"  class=\"mtq_preload\">\r\n    R\u00e9ponse partielle    <\/div> <div id=\"mtq_exit_warning_string\"  class=\"mtq_preload\">\r\n    Vous n'avez pas fini votre quiz. Si vous quittez cette page, votre progression sera perdue.    <\/div> <div id='mtq_correct_answer_string' class='mtq_preload'>\r\n    R\u00e9ponses correctes    <\/div> <div id='mtq_you_selected_string' class='mtq_preload'>\r\n    Vous avez s\u00e9lectionn\u00e9    <\/div> <div id='mtq_not_attempted_string' class='mtq_preload'>\r\n    Pas essayer    <\/div> <div id='mtq_final_score_on_quiz_string' class='mtq_preload'>\r\n    Score final du quiz    <\/div> <div id='mtq_attempted_questions_correct_string' class='mtq_preload'>\r\n    Nombre de questions r\u00e9pondues de mani\u00e8re correcte    <\/div> <div id='mtq_attempted_questions_wrong_string' class='mtq_preload'>\r\n    Nombre de questions r\u00e9pondues de mani\u00e8re incorrecte    <\/div> <div id='mtq_questions_not_attempted_string' class='mtq_preload'>\r\n    Question non r\u00e9pondues    <\/div> <div id='mtq_total_questions_on_quiz_string' class='mtq_preload'>\r\n    Nombre total de questions dans le quiz    <\/div> <div id='mtq_question_details_string' class='mtq_preload'>\r\n    D\u00e9tail de la question    <\/div> <div id='mtq_quiz_results_string' class='mtq_preload'>\r\n    R\u00e9sultats    <\/div> <div id='mtq_date_string' class='mtq_preload'>\r\n    Date    <\/div> <div id='mtq_score_string' class='mtq_preload'>\r\n    Score    <\/div> <div id='mtq_hint_string' class='mtq_preload'>\r\n    Indice    <\/div>\r\n    <div id='mtq_time_allowed_string' class='mtq_preload'>Temps autoris\u00e9<\/div>\r\n<div id='mtq_minutes_string' class='mtq_preload'>minutes<\/div>\r\n<div id='mtq_seconds_string' class='mtq_preload'>secondes<\/div>\r\n<div id='mtq_time_used_string' class='mtq_preload'>Temps utilis\u00e9<\/div>\r\n<div id='mtq_answer_choices_selected_string' class='mtq_preload'>R\u00e9ponse(s) s\u00e9lectionn\u00e9e(s)<\/div>\r\n<div id='mtq_question_text_string' class='mtq_preload'>Texte de la question<\/div>\r\n\r\n\r\n    <input type='hidden' id='mtq_answer_display-1' value='2'\/>\r\n    <input type='hidden' id='mtq_autoadvance-1' value='0'\/>\r\n    <input type='hidden' id='mtq_autosubmit-1' value='0'\/>\r\n    <input type='hidden' id='mtq_single_page-1' value='1'\/>\r\n    <input type='hidden' id='mtq_show_hints-1' value='0'\/>\r\n    <input type='hidden' id='mtq_show_start-1' value='1'\/>\r\n    <input type='hidden' id='mtq_show_final-1' value='1'\/>\r\n    <input type='hidden' id='mtq_show_alerts-1' value='1'\/>\r\n    <input type='hidden' id='mtq_multiple_chances-1' value='0'\/>\r\n    <input type='hidden' id='mtq_proofread-1' value='0'\/>\r\n    <input type='hidden' id='mtq_scoring-1' value='0'\/>\r\n    <input type='hidden' id='mtq_vform-1' value='1'\/>\r\n    <input type=\"hidden\" name=\"quiz_id\" id=\"quiz_id-1\" value=\"7\" \/>\r\n    <input type=\"hidden\" name=\"mtq_total_questions\" id=\"mtq_total_questions-1\" value=\"5\" \/>\r\n    <input type=\"hidden\" name=\"mtq_current_score\" id=\"mtq_current_score-1\" value=\"0\" \/>\r\n    <input type=\"hidden\" name=\"mtq_max_score\" id=\"mtq_max_score-1\" value=\"0\" \/>\r\n    <input type=\"hidden\" name=\"mtq_questions_attempted\" id=\"mtq_questions_attempted-1\" value=\"0\" \/>\r\n    <input type=\"hidden\" name=\"mtq_questions_correct\" id=\"mtq_questions_correct-1\" value=\"0\" \/>\r\n    <input type=\"hidden\" name=\"mtq_questions_wrong\" id=\"mtq_questions_wrong-1\" value=\"0\" \/>\r\n    <input type=\"hidden\" name=\"mtq_questions_not_attempted\" id=\"mtq_questions_not_attempted-1\" value=\"0\" \/>\r\n    <input type=\"hidden\" id=\"mtq_display_number-1\" value=\"1\" \/>\r\n    <input type=\"hidden\" id=\"mtq_show_list_option-1\" value=\"0\" \/>\r\n    <input type=\"hidden\" id=\"mtq_show_stamps-1\" value=\"1\" \/>\r\n    <input type='hidden' id='mtq_num_ratings-1' value='6'\/><input type='hidden' id='mtq_ratingval-1-1' value='-1'\/><div id='mtq_rating-1-1' class='mtq_preload'>Fini<\/div><input type='hidden' id='mtq_ratingval-2-1' value='0'\/><div id='mtq_rating-2-1' class='mtq_preload'>Vous avez besoin de plus d'entra\u00eenement !<\/div><input type='hidden' id='mtq_ratingval-3-1' value='40'\/><div id='mtq_rating-3-1' class='mtq_preload'>Pers\u00e9v\u00e9rez !<\/div><input type='hidden' id='mtq_ratingval-4-1' value='60'\/><div id='mtq_rating-4-1' class='mtq_preload'>Pas mal !<\/div><input type='hidden' id='mtq_ratingval-5-1' value='80'\/><div id='mtq_rating-5-1' class='mtq_preload'>Bon travail !<\/div><input type='hidden' id='mtq_ratingval-6-1' value='100'\/><div id='mtq_rating-6-1' class='mtq_preload'>Parfait !<\/div>    <input type=\"hidden\" id=\"mtq_gf_present-1\" value=\"0\"\/>\r\n    <input type=\"hidden\" id=\"mtq_cf7_present-1\" value=\"0\"\/>\r\n    <input type=\"hidden\" id=\"mtq_quiz_in_form-1\" value=\"0\"\/>\r\n    <input type=\"hidden\" id=\"mtq_gf_formid_number-1\" value=\"\"\/>\r\n\r\n  <\/div>\r\n  \r\n  <!--Variables Div--> \r\n  <!--\/form--> \r\n<\/div>\r\n<!--Quiz area div-->\r\n\r\n\n<p><img loading=\"lazy\" class=\"alignnone 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