Quiz — 253.._Magazine 18_4Sc_19-20 (Logarithme).pdf

Question 1 sur 10 20:00

[{"id":21679,"question":"Quelle est la valeur de log₁₀(100) ?","option_a":"1","option_b":"2","option_c":"10","option_d":"100","option_e":"","option_f":"","bonne_reponse":"b","explication":"log₁₀(100) = 2 car 10² = 100.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"1\", \"b\": \"2\", \"c\": \"10\", \"d\": \"100\"}}","_debug_options_count":4},{"id":21680,"question":"L'expression logₐ(b) + logₐ(c) est égale à :","option_a":"logₐ(b + c)","option_b":"logₐ(b·c)","option_c":"logₐ(b - c)","option_d":"logₐ(b\/c)","option_e":"","option_f":"","bonne_reponse":"b","explication":"C'est une propriété fondamentale des logarithmes : logₐ(b) + logₐ(c) = logₐ(b·c).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"logₐ(b + c)\", \"b\": \"logₐ(b·c)\", \"c\": \"logₐ(b - c)\", \"d\": \"","_debug_options_count":4},{"id":21681,"question":"Vrai ou Faux : La fonction logarithme est définie pour tout nombre réel positif.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction logarithme est définie uniquement pour les nombres réels strictement positifs.","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":21682,"question":"Quelle est la dérivée de f(x) = ln(x) ?","option_a":"1\/x","option_b":"x","option_c":"1","option_d":"ln(x)\/x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(x) est 1\/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\": \"1\/x\", \"b\": \"x\", \"c\": \"1\", \"d\": \"ln(x)\/x\"}}","_debug_options_count":4},{"id":21683,"question":"Résoudre l'équation log₂(x) = 3.","option_a":"x = 6","option_b":"x = 8","option_c":"x = 9","option_d":"x = 1\/8","option_e":"","option_f":"","bonne_reponse":"b","explication":"log₂(x) = 3 ⇒ x = 2³ = 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 = 1\/8\"}}","_debug_options_count":4},{"id":21684,"question":"Vrai ou Faux : logₐ(1) = 0 pour tout a \u003E 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"logₐ(1) = 0 car a⁰ = 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":21685,"question":"Quelle propriété permet d'écrire logₐ(b) = ln(b)\/ln(a) ?","option_a":"Propriété de changement de base","option_b":"Propriété des puissances","option_c":"Propriété des racines","option_d":"Propriété des logarithmes naturels","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est la propriété de changement de base : logₐ(b) = ln(b)\/ln(a).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Propriété de changement de base\", \"b\": \"Propriété des puissan","_debug_options_count":4},{"id":21686,"question":"Résoudre l'équation ln(x) = ln(5) + ln(2).","option_a":"x = 7","option_b":"x = 10","option_c":"x = 3","option_d":"x = 1\/10","option_e":"","option_f":"","bonne_reponse":"b","explication":"ln(x) = ln(5·2) ⇒ x = 10.","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 = 7\", \"b\": \"x = 10\", \"c\": \"x = 3\", \"d\": \"x = 1\/10\"}}","_debug_options_count":4},{"id":21687,"question":"Vrai ou Faux : La fonction logarithme est croissante sur son ensemble de définition.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction logarithme est strictement croissante sur ℝ⁺*.","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":21688,"question":"Quelle est la valeur de log₃(1\/9) ?","option_a":"-2","option_b":"-1","option_c":"1","option_d":"2","option_e":"","option_f":"","bonne_reponse":"a","explication":"log₃(1\/9) = log₃(3⁻²) = -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\": \"-1\", \"c\": \"1\", \"d\": \"2\"}}","_debug_options_count":4}]