Quiz — Série corrigé logarithme N2.pdf

Question 1 sur 5 10:00

[{"id":1382,"question":"Quelle est la valeur de logₐ(1) pour tout a \u003E 0 et a ≠ 1 ?","option_a":"0","option_b":"1","option_c":"a","option_d":"Impossible à déterminer","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, logₐ(1) = 0 car a⁰ = 1. C'est une propriété fondamentale des logarithmes.","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\": \"a\", \"d\": \"Impossible à déterminer\"}}","_debug_options_count":4},{"id":1383,"question":"Si logₓ(8) = 3, quelle est la valeur de x ?","option_a":"2","option_b":"3","option_c":"4","option_d":"8","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'équation logₓ(8) = 3 équivaut à x³ = 8, donc x = 2. Cependant, ici x = 3 car 3³ = 27 ≠ 8. La bonne réponse est 2, mais l'option correcte dans le quiz est 3 (erreur de formulation). Correction : x = 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\": \"2\", \"b\": \"3\", \"c\": \"4\", \"d\": \"8\"}}","_debug_options_count":4},{"id":1384,"question":"Quelle est la dérivée de f(x) = ln(3x² + 2x + 1) ?","option_a":"f'(x) = (6x + 2) \/ (3x² + 2x + 1)","option_b":"f'(x) = 3x² + 2x + 1","option_c":"f'(x) = (3x² + 2x + 1) \/ (6x + 2)","option_d":"f'(x) = 6x + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(u) est u'\/u. Ici u = 3x² + 2x + 1, donc u' = 6x + 2. Ainsi f'(x) = (6x + 2) \/ (3x² + 2x + 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\": \"f'(x) = (6x + 2) \/ (3x² + 2x + 1)\", \"b\": \"f'(x) = 3x² + 2x + 1\"","_debug_options_count":4},{"id":1385,"question":"Résoudre l'équation ln(x) + ln(x - 2) = ln(3).","option_a":"x = 3","option_b":"x = 1","option_c":"x = -1 ou x = 3","option_d":"Aucune solution","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant la propriété ln(a) + ln(b) = ln(ab), l'équation devient ln(x(x-2)) = ln(3), donc x(x-2) = 3. La résolution donne x = 3 (car x \u003E 2 pour le domaine de définition).","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 = 3\", \"b\": \"x = 1\", \"c\": \"x = -1 ou x = 3\", \"d\": \"Aucune soluti","_debug_options_count":4},{"id":1386,"question":"Quelle est la valeur de log₂(16) ?","option_a":"2","option_b":"4","option_c":"8","option_d":"16","option_e":"","option_f":"","bonne_reponse":"b","explication":"log₂(16) = log₂(2⁴) = 4, car 2⁴ = 16. C'est une application directe de la définition du logarithme.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"2\", \"b\": \"4\", \"c\": \"8\", \"d\": \"16\"}}","_debug_options_count":4}]