Quiz — énoncé_Fonctions-logarithmes (1) (1).pdf

Question 1 sur 5 10:00

[{"id":1854,"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·ln(e) = 3·1 = 3, car ln(e) = 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\": \"3\", \"b\": \"e^3\", \"c\": \"0\", \"d\": \"1\"}}","_debug_options_count":4},{"id":1855,"question":"Quelle est la solution de l'équation ln(x) = 2 ?","option_a":"x = e^2","option_b":"x = 2","option_c":"x = ln(2)","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"a","explication":"En appliquant la fonction exponentielle des deux côtés, on obtient x = e^2.","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 = e^2\", \"b\": \"x = 2\", \"c\": \"x = ln(2)\", \"d\": \"x = 0\"}}","_debug_options_count":4},{"id":1856,"question":"Quelle est la dérivée de f(x) = ln(2x + 1) ?","option_a":"f'(x) = 1\/(2x + 1)","option_b":"f'(x) = 2\/(2x + 1)","option_c":"f'(x) = 2x\/(2x + 1)","option_d":"f'(x) = 1\/x","option_e":"","option_f":"","bonne_reponse":"b","explication":"En utilisant la règle de la chaîne, f'(x) = (1\/(2x + 1)) · 2 = 2\/(2x + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"f'(x) = 1\/(2x + 1)\", \"b\": \"f'(x) = 2\/(2x + 1)\", \"c\": \"f'(x) = 2x\/","_debug_options_count":4},{"id":1857,"question":"Quelle est la valeur de log_10(1000) ?","option_a":"3","option_b":"100","option_c":"10","option_d":"0","option_e":"","option_f":"","bonne_reponse":"a","explication":"log_10(1000) = log_10(10^3) = 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\", \"b\": \"100\", \"c\": \"10\", \"d\": \"0\"}}","_debug_options_count":4},{"id":1858,"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":"b","explication":"La fonction ln(x) tend vers -∞ lorsque x tend vers 0 par la droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0\", \"b\": \"-∞\", \"c\": \"+∞\", \"d\": \"1\"}}","_debug_options_count":4}]