Quiz — série26-logarithme corrigé.pdf

Question 1 sur 10 20:00

[{"id":30970,"question":"Quelle est la valeur de ln(e^3) ?","option_a":"3","option_b":"e^3","option_c":"0","option_d":"1","option_e":"","option_f":"","bonne_reponse":"a","explication":"ln(e^3) = 3 car ln et e sont des fonctions réciproques.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"3\", \"b\": \"e^3\", \"c\": \"0\", \"d\": \"1\"}}","_debug_options_count":4},{"id":30971,"question":"La fonction logarithme est-elle définie pour x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction logarithme est définie uniquement pour x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":30972,"question":"Quelle est la dérivée de la fonction f(x) = ln(2x) ?","option_a":"1\/(2x)","option_b":"2\/x","option_c":"1\/x","option_d":"2\/(2x)","option_e":"","option_f":"","bonne_reponse":"c","explication":"La dérivée de ln(2x) est (1\/(2x)) * 2 = 1\/x (dérivée d'une fonction composée).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"1\/(2x)\", \"b\": \"2\/x\", \"c\": \"1\/x\", \"d\": \"2\/(2x)\"}}","_debug_options_count":4},{"id":30973,"question":"L'équation ln(x) = -2 admet-elle une solution ?","option_a":"Oui, x = e^(-2)","option_b":"Non, car ln(x) est toujours positif","option_c":"Oui, x = -2","option_d":"Non, car x doit être positif","option_e":"","option_f":"","bonne_reponse":"a","explication":"ln(x) = -2 admet une solution x = e^(-2) car ln est défini pour x \u003E 0 et peut prendre des valeurs négatives.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Oui, x = e^(-2)\", \"b\": \"Non, car ln(x) est toujours positif\", \"c\"","_debug_options_count":4},{"id":30974,"question":"La propriété ln(a) + ln(b) = ln(ab) est-elle toujours vraie ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Cette propriété est vraie uniquement si a \u003E 0 et b \u003E 0. Elle n'est pas valable pour des nombres négatifs ou nuls.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":30975,"question":"Quelle est la limite de ln(x) lorsque x tend vers 0+ ?","option_a":"0","option_b":"+∞","option_c":"-∞","option_d":"1","option_e":"","option_f":"","bonne_reponse":"c","explication":"La limite de ln(x) lorsque x tend vers 0+ est -∞ car ln(x) décroît indéfiniment vers les valeurs négatives.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0\", \"b\": \"+∞\", \"c\": \"-∞\", \"d\": \"1\"}}","_debug_options_count":4},{"id":30976,"question":"Résoudre l'inéquation ln(x) \u003E 1.","option_a":"x \u003E e","option_b":"x \u003E 1","option_c":"x \u003C e","option_d":"x \u003C 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"ln(x) \u003E 1 équivaut à x \u003E e^1 = e, car la fonction ln est croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x \u003E e\", \"b\": \"x \u003E 1\", \"c\": \"x \u003C e\", \"d\": \"x \u003C 1\"}}","_debug_options_count":4},{"id":30977,"question":"La fonction f(x) = ln(x^2) est-elle définie pour x = -1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Oui, car x^2 \u003E 0 pour tout x ≠ 0, donc ln(x^2) est défini pour x = -1 (f(-1) = ln(1) = 0).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":30978,"question":"Quelle est la valeur de ln(1) ?","option_a":"0","option_b":"1","option_c":"e","option_d":"-1","option_e":"","option_f":"","bonne_reponse":"a","explication":"ln(1) = 0 car e^0 = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"e\", \"d\": \"-1\"}}","_debug_options_count":4},{"id":30979,"question":"La fonction logarithme est-elle croissante sur son ensemble de définition ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Oui, la fonction logarithme est strictement croissante sur ]0, +∞[.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]