Quiz — Série corrigé logarithme N1.pdf

Question 1 sur 10 20:00

[{"id":5306,"question":"Quelle est la valeur de log₅(25) ?","option_a":"2","option_b":"5","option_c":"0","option_d":"1","option_e":"","option_f":"","bonne_reponse":"a","explication":"log₅(25) = log₅(5²) = 2, car 5² = 25. La bonne réponse est donc 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\": \"2\", \"b\": \"5\", \"c\": \"0\", \"d\": \"1\"}}","_debug_options_count":4},{"id":5307,"question":"La propriété log(a + b) = log(a) + log(b) est-elle vraie ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Cette propriété est fausse. La bonne propriété est log(ab) = log(a) + log(b), mais pas pour une somme.","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":5308,"question":"Résolvez l'équation : log₂(x) = 3.","option_a":"x = 6","option_b":"x = 8","option_c":"x = 9","option_d":"x = 12","option_e":"","option_f":"","bonne_reponse":"b","explication":"log₂(x) = 3 équivaut à x = 2³ = 8. La bonne réponse est donc x = 8.","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 = 6\", \"b\": \"x = 8\", \"c\": \"x = 9\", \"d\": \"x = 12\"}}","_debug_options_count":4},{"id":5309,"question":"Quelle est la dérivée de f(x) = ln(3x + 1) ?","option_a":"f'(x) = 3\/(3x + 1)","option_b":"f'(x) = 1\/(3x + 1)","option_c":"f'(x) = 3x\/(3x + 1)","option_d":"f'(x) = 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. Ainsi, f'(x) = 3\/(3x + 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) = 3\/(3x + 1)\", \"b\": \"f'(x) = 1\/(3x + 1)\", \"c\": \"f'(x) = 3x\/","_debug_options_count":4},{"id":5310,"question":"L'inéquation log₁₀(x) \u003E 2 a pour solution :","option_a":"x \u003E 100","option_b":"x \u003E 20","option_c":"x \u003E 10","option_d":"x \u003E 0","option_e":"","option_f":"","bonne_reponse":"a","explication":"log₁₀(x) \u003E 2 équivaut à x \u003E 10² = 100. La solution est donc x \u003E 100.","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 100\", \"b\": \"x \u003E 20\", \"c\": \"x \u003E 10\", \"d\": \"x \u003E 0\"}}","_debug_options_count":4},{"id":5311,"question":"La fonction f(x) = log(x) est-elle définie pour x = -1 ?","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. x = -1 n'est pas dans 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\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":5312,"question":"Quelle est la valeur de log₃(1\/9) ?","option_a":"-2","option_b":"2","option_c":"-1","option_d":"0","option_e":"","option_f":"","bonne_reponse":"a","explication":"log₃(1\/9) = log₃(3⁻²) = -2, car 3⁻² = 1\/9. La bonne réponse est donc -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\": \"-2\", \"b\": \"2\", \"c\": \"-1\", \"d\": \"0\"}}","_debug_options_count":4},{"id":5313,"question":"La dérivée de f(x) = log(x² + 1) est :","option_a":"f'(x) = 2x\/(x² + 1)","option_b":"f'(x) = 1\/(x² + 1)","option_c":"f'(x) = x\/(x² + 1)","option_d":"f'(x) = 2\/(x² + 1)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de log(u(x)) est u'(x)\/u(x). Ici, u(x) = x² + 1, donc u'(x) = 2x. Ainsi, f'(x) = 2x\/(x² + 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) = 2x\/(x² + 1)\", \"b\": \"f'(x) = 1\/(x² + 1)\", \"c\": \"f'(x) = ","_debug_options_count":4},{"id":5314,"question":"Résolvez l'inéquation : log₅(x) ≤ 1.","option_a":"0 \u003C x ≤ 5","option_b":"x ≤ 5","option_c":"x ≥ 5","option_d":"x \u003E 0","option_e":"","option_f":"","bonne_reponse":"a","explication":"log₅(x) ≤ 1 équivaut à x ≤ 5¹ = 5, avec x \u003E 0. La solution est donc 0 \u003C x ≤ 5.","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 \u003C x ≤ 5\", \"b\": \"x ≤ 5\", \"c\": \"x ≥ 5\", \"d\": \"x \u003E 0\"}}","_debug_options_count":4},{"id":5315,"question":"La propriété log(a^b) = b·log(a) est-elle toujours vraie ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Cette propriété est vraie pour tout a \u003E 0 et tout réel b. Elle est donc toujours valable dans le domaine de définition du logarithme.","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}]