Quiz — 192.._Magazine-25 FONCTIONS LOGARITHMES 2.pdf

Question 1 sur 10 20:00

[{"id":21109,"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":"Par définition, 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":21110,"question":"Si ln(x) = ln(5) + ln(2), alors x est égal à :","option_a":"10","option_b":"7","option_c":"ln(7)","option_d":"ln(10)","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant la propriété ln(ab) = ln(a) + ln(b), on obtient ln(x) = ln(10), donc x = 10.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"10\", \"b\": \"7\", \"c\": \"ln(7)\", \"d\": \"ln(10)\"}}","_debug_options_count":4},{"id":21111,"question":"Vrai ou Faux : La fonction ln(x) est définie pour tout x réel.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction ln(x) n'est définie que 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":21112,"question":"Quelle est la dérivée de la fonction f(x) = ln(3x + 1) ?","option_a":"3\/(3x + 1)","option_b":"1\/(3x + 1)","option_c":"3x\/(3x + 1)","option_d":"1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(u(x)) est u'(x)\/u(x). Ici, u(x) = 3x + 1, donc u'(x) = 3.","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\/(3x + 1)\", \"b\": \"1\/(3x + 1)\", \"c\": \"3x\/(3x + 1)\", \"d\": \"1\"}}","_debug_options_count":4},{"id":21113,"question":"Résoudre l'inéquation ln(x) \u003C 2.","option_a":"x \u003C e^2","option_b":"0 \u003C x \u003C e^2","option_c":"x \u003E e^2","option_d":"x ∈ ℝ","option_e":"","option_f":"","bonne_reponse":"b","explication":"ln(x) \u003C 2 équivaut à x \u003C e^2, mais comme ln(x) est défini pour x \u003E 0, la solution est 0 \u003C x \u003C e^2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"x \u003C e^2\", \"b\": \"0 \u003C x \u003C e^2\", \"c\": \"x \u003E e^2\", \"d\": \"x ∈ ℝ\"}}","_debug_options_count":4},{"id":21114,"question":"Vrai ou Faux : ln(e^x) = x pour tout x réel.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, ln(e^x) = x car e^x est l'exponentielle de x.","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":21115,"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":"Lorsque x tend vers 0+, ln(x) tend vers -∞.","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":21116,"question":"Si ln(a) = 2 et ln(b) = 3, alors ln(a\/b) est égal à :","option_a":"-1","option_b":"5","option_c":"1","option_d":"-5","option_e":"","option_f":"","bonne_reponse":"a","explication":"ln(a\/b) = ln(a) - ln(b) = 2 - 3 = -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\": \"-1\", \"b\": \"5\", \"c\": \"1\", \"d\": \"-5\"}}","_debug_options_count":4},{"id":21117,"question":"Vrai ou Faux : La fonction ln(x) est croissante sur son domaine de définition.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(x) est 1\/x \u003E 0 pour x \u003E 0, donc la fonction 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":21118,"question":"Quelle est la solution de l'équation ln(x^2) = 4 ?","option_a":"x = e^2","option_b":"x = ±e^2","option_c":"x = 2e","option_d":"x = e^4","option_e":"","option_f":"","bonne_reponse":"b","explication":"ln(x^2) = 4 équivaut à 2·ln(|x|) = 4, donc ln(|x|) = 2, soit |x| = e^2. Les solutions sont x = e^2 ou x = -e^2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"x = e^2\", \"b\": \"x = ±e^2\", \"c\": \"x = 2e\", \"d\": \"x = e^4\"}}","_debug_options_count":4}]