Quiz — 64020284c5eb3_corrigé_Fonction Logarithme.pdf

Question 1 sur 10 20:00

[{"id":29220,"question":"Quelle est la valeur de log(100) si log(10) = 1 ?","option_a":"1","option_b":"2","option_c":"10","option_d":"0","option_e":"","option_f":"","bonne_reponse":"b","explication":"log(100) = log(10²) = 2·log(10) = 2·1 = 2. Utilisez la propriété log(a^n) = n·log(a).","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\": \"0\"}}","_debug_options_count":4},{"id":29221,"question":"La fonction logarithme est-elle 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 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\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":29222,"question":"Quelle est la dérivée de f(x) = ln(3x² + 2x) ?","option_a":"(6x + 2)\/(3x² + 2x)","option_b":"(6x + 2)","option_c":"3x² + 2x","option_d":"(3x² + 2x)\/(6x + 2)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(u(x)) est u'(x)\/u(x). Ici, u(x) = 3x² + 2x, donc u'(x) = 6x + 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\": \"(6x + 2)\/(3x² + 2x)\", \"b\": \"(6x + 2)\", \"c\": \"3x² + 2x\", \"d\": \"(","_debug_options_count":4},{"id":29223,"question":"L'équation log(x) = 2 a pour solution x = 100.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"log(x) = 2 ⇒ x = 10² = 100. La solution est donc correcte.","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":29224,"question":"Quelle propriété permet d'écrire log(8) = 3·log(2) ?","option_a":"log(a + b) = log(a) + log(b)","option_b":"log(a^n) = n·log(a)","option_c":"log(a\/b) = log(a) - log(b)","option_d":"log(ab) = log(a) + log(b)","option_e":"","option_f":"","bonne_reponse":"b","explication":"La propriété log(a^n) = n·log(a) permet de factoriser l'exposant dans le 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\": \"log(a + b) = log(a) + log(b)\", \"b\": \"log(a^n) = n·log(a)\", \"c\": ","_debug_options_count":4},{"id":29225,"question":"La fonction f(x) = ln(x) est-elle croissante sur son domaine de définition ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(x) est 1\/x, qui est positive pour x \u003E 0. La fonction est donc croissante.","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":29226,"question":"Résoudre l'inéquation log(x - 1) \u003E 0.","option_a":"x \u003E 1","option_b":"x \u003E 2","option_c":"x \u003E 0","option_d":"x \u003E 10","option_e":"","option_f":"","bonne_reponse":"b","explication":"log(x - 1) \u003E 0 ⇒ x - 1 \u003E 10⁰ ⇒ x - 1 \u003E 1 ⇒ x \u003E 2. N'oubliez pas le domaine de définition x - 1 \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\": \"x \u003E 1\", \"b\": \"x \u003E 2\", \"c\": \"x \u003E 0\", \"d\": \"x \u003E 10\"}}","_debug_options_count":4},{"id":29227,"question":"La fonction logarithme népérien est-elle l'inverse de la fonction exponentielle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Oui, ln et exp sont des fonctions réciproques : ln(exp(x)) = x et exp(ln(x)) = x pour x \u003E 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},{"id":29228,"question":"Quelle est la valeur de log(0.01) si log(10) = 1 ?","option_a":"-2","option_b":"2","option_c":"-1","option_d":"0.01","option_e":"","option_f":"","bonne_reponse":"a","explication":"log(0.01) = log(10⁻²) = -2·log(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\": \"a\", \"options\": {\"a\": \"-2\", \"b\": \"2\", \"c\": \"-1\", \"d\": \"0.01\"}}","_debug_options_count":4},{"id":29229,"question":"La dérivée de f(x) = ln(x²) est-elle égale à 2\/x ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(x²) est 2x\/x² = 2\/x. La réponse est donc correcte.","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}]