Quiz — 242.._Magazine 16_4Sc_19-20 (Logarithme).pdf

Question 1 sur 10 20:00

[{"id":19109,"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. 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\": \"1\", \"b\": \"2\", \"c\": \"10\", \"d\": \"100\"}}","_debug_options_count":4},{"id":19110,"question":"Si logₐ(b) = c, alors a^c = b.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est vrai : par définition, logₐ(b) = c signifie que a^c = b.","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":19111,"question":"Quelle propriété est correcte pour logₐ(x) + logₐ(y) ?","option_a":"logₐ(x + y)","option_b":"logₐ(x * y)","option_c":"logₐ(x \/ y)","option_d":"logₐ(x) * logₐ(y)","option_e":"","option_f":"","bonne_reponse":"b","explication":"La propriété est logₐ(x * y) = logₐ(x) + logₐ(y), valable pour x \u003E 0 et y \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\": \"logₐ(x + y)\", \"b\": \"logₐ(x * y)\", \"c\": \"logₐ(x \/ y)\", \"d\": ","_debug_options_count":4},{"id":19112,"question":"L'équation log₃(x) = 4 admet pour solution :","option_a":"x = 3⁴","option_b":"x = 4³","option_c":"x = 12","option_d":"x = 81","option_e":"","option_f":"","bonne_reponse":"a","explication":"log₃(x) = 4 ⇒ x = 3⁴ = 81. La solution est x = 81.","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 = 3⁴\", \"b\": \"x = 4³\", \"c\": \"x = 12\", \"d\": \"x = 81\"}}","_debug_options_count":4},{"id":19113,"question":"Pour tout a \u003E 0 et a ≠ 1, logₐ(1) = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est vrai : a⁰ = 1, donc logₐ(1) = 0 par 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":19114,"question":"Quelle est la dérivée de f(x) = ln(x) ?","option_a":"1\/x","option_b":"x","option_c":"ln(x)\/x","option_d":"1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(x) est 1\/x, une propriété fondamentale des logarithmes naturels.","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\": \"ln(x)\/x\", \"d\": \"1\"}}","_debug_options_count":4},{"id":19115,"question":"Résoudre l'inéquation log₂(x) \u003E 3.","option_a":"x \u003E 8","option_b":"x \u003C 8","option_c":"x \u003E 2³","option_d":"x \u003C 2³","option_e":"","option_f":"","bonne_reponse":"a","explication":"log₂(x) \u003E 3 ⇒ x \u003E 2³ ⇒ x \u003E 8. La solution est x \u003E 8.","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 8\", \"b\": \"x \u003C 8\", \"c\": \"x \u003E 2³\", \"d\": \"x \u003C 2³\"}}","_debug_options_count":4},{"id":19116,"question":"La fonction logₐ(x) est définie pour x ≤ 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Faux : la fonction logₐ(x) n'est définie que pour x \u003E 0, car a^y \u003E 0 pour tout y réel.","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":19117,"question":"Quelle est la valeur de log₅(125) ?","option_a":"3","option_b":"5","option_c":"25","option_d":"1\/3","option_e":"","option_f":"","bonne_reponse":"a","explication":"log₅(125) = 3 car 5³ = 125. C'est une application directe de la 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\": \"3\", \"b\": \"5\", \"c\": \"25\", \"d\": \"1\/3\"}}","_debug_options_count":4},{"id":19118,"question":"L'équation logₓ(16) = 2 admet pour solution :","option_a":"x = 2","option_b":"x = 4","option_c":"x = 8","option_d":"x = 16","option_e":"","option_f":"","bonne_reponse":"b","explication":"logₓ(16) = 2 ⇒ x² = 16 ⇒ x = 4 (car x \u003E 0 et x ≠ 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\": \"x = 2\", \"b\": \"x = 4\", \"c\": \"x = 8\", \"d\": \"x = 16\"}}","_debug_options_count":4}]