Quiz — التمرين 2 لوغاريتم.pdf

Question 1 sur 10 20:00

[{"id":29880,"question":"Quelle est la valeur de log₁₀(100) ?","option_a":"0","option_b":"1","option_c":"2","option_d":"10","option_e":"","option_f":"","bonne_reponse":"c","explication":"log₁₀(100) = log₁₀(10²) = 2·log₁₀(10) = 2·1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"2\", \"d\": \"10\"}}","_debug_options_count":4},{"id":29881,"question":"L'expression logₐ(b·c) est égale à logₐ(b) + logₐ(c).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une propriété fondamentale des logarithmes : logₐ(b·c) = logₐ(b) + logₐ(c).","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":29882,"question":"Résolvez l'équation : ln(x) = 3.","option_a":"x = e³","option_b":"x = 3","option_c":"x = ln(3)","option_d":"x = 10³","option_e":"","option_f":"","bonne_reponse":"a","explication":"ln(x) = 3 ⇒ x = e³ (par définition de la fonction logarithme népérien).","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 = e³\", \"b\": \"x = 3\", \"c\": \"x = ln(3)\", \"d\": \"x = 10³\"}}","_debug_options_count":4},{"id":29883,"question":"Quelle propriété permet de simplifier logₐ(aⁿ) ?","option_a":"logₐ(a) + logₐ(n)","option_b":"n·logₐ(a)","option_c":"logₐ(a) - logₐ(n)","option_d":"logₐ(n)","option_e":"","option_f":"","bonne_reponse":"b","explication":"La propriété logₐ(aⁿ) = n·logₐ(a) permet de simplifier cette expression.","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(a) + logₐ(n)\", \"b\": \"n·logₐ(a)\", \"c\": \"logₐ(a) - lo","_debug_options_count":4},{"id":29884,"question":"L'équation 2ˣ = 8 a pour solution x = 3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"2ˣ = 8 ⇒ 2ˣ = 2³ ⇒ x = 3. L'affirmation est donc vraie.","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":29885,"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·log₂(2) = 4·1 = 4.","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},{"id":29886,"question":"La fonction logarithme est définie pour tous les nombres réels.","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 les nombres strictement positifs (x \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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":29887,"question":"Quelle est la dérivée de la fonction f(x) = ln(x) ?","option_a":"1\/x","option_b":"x","option_c":"eˣ","option_d":"1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(x) est 1\/x, une propriété fondamentale en analyse.","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\": \"eˣ\", \"d\": \"1\"}}","_debug_options_count":4},{"id":29888,"question":"Résolvez l'équation : log₃(x) = 2.","option_a":"x = 6","option_b":"x = 9","option_c":"x = 3²","option_d":"x = 1\/9","option_e":"","option_f":"","bonne_reponse":"c","explication":"log₃(x) = 2 ⇒ x = 3² = 9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"x = 6\", \"b\": \"x = 9\", \"c\": \"x = 3²\", \"d\": \"x = 1\/9\"}}","_debug_options_count":4},{"id":29889,"question":"La propriété logₐ(1) = 0 est-elle toujours vraie ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Oui, car a⁰ = 1 pour tout a \u003E 0 et a ≠ 1. Donc logₐ(1) = 0.","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}]