Quiz — série24-logarithme corrigé.pdf

Question 1 sur 10 20:00

[{"id":30940,"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. Le logarithme décimal de 100 est donc 2.","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":30941,"question":"Si ln(x) = 3, alors x est égal à :","option_a":"e³","option_b":"3e","option_c":"e\/3","option_d":"ln(3)","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, si ln(x) = a, alors x = eᵃ. Ici, x = e³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"e³\", \"b\": \"3e\", \"c\": \"e\/3\", \"d\": \"ln(3)\"}}","_debug_options_count":4},{"id":30942,"question":"La fonction logarithme népérien est définie pour :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction ln(x) est définie uniquement pour x \u003E 0. Elle n'est pas définie pour les valeurs négatives ou nulles.","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":30943,"question":"Quelle propriété est correcte pour tout a \u003E 0 et b \u003E 0 ?","option_a":"log(a + b) = log(a) + log(b)","option_b":"log(ab) = log(a) + log(b)","option_c":"log(a\/b) = log(a) - log(b²)","option_d":"log(aⁿ) = n log(a²)","option_e":"","option_f":"","bonne_reponse":"b","explication":"La propriété correcte est log(ab) = log(a) + log(b), qui découle de la définition du logarithme comme fonction exponentielle inverse.","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(ab) = log(a) + log(b)\", ","_debug_options_count":4},{"id":30944,"question":"L'équation log₁₀(x) = -2 admet pour solution :","option_a":"x = 0.01","option_b":"x = -20","option_c":"x = 1\/100","option_d":"x = 100","option_e":"","option_f":"","bonne_reponse":"a","explication":"log₁₀(x) = -2 ⇒ x = 10⁻² = 0.01. Les autres options sont incorrectes ou hors domaine de 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\": \"x = 0.01\", \"b\": \"x = -20\", \"c\": \"x = 1\/100\", \"d\": \"x = 100\"}}","_debug_options_count":4},{"id":30945,"question":"La dérivée de ln(x) est :","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. Cette 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":30946,"question":"Quelle est la solution de l'équation ln(2x + 1) = 0 ?","option_a":"x = 0","option_b":"x = 1","option_c":"x = -0.5","option_d":"x = 0.5","option_e":"","option_f":"","bonne_reponse":"a","explication":"ln(2x + 1) = 0 ⇒ 2x + 1 = e⁰ = 1 ⇒ 2x = 0 ⇒ x = 0. La solution est donc x = 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\": \"x = 0\", \"b\": \"x = 1\", \"c\": \"x = -0.5\", \"d\": \"x = 0.5\"}}","_debug_options_count":4},{"id":30947,"question":"Pour a \u003E 0, logₐ(a) est égal à :","option_a":"0","option_b":"1","option_c":"a","option_d":"log(a)","option_e":"","option_f":"","bonne_reponse":"b","explication":"Par définition, logₐ(a) = 1 car a¹ = a. Cette propriété est fondamentale pour les logarithmes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"a\", \"d\": \"log(a)\"}}","_debug_options_count":4},{"id":30948,"question":"La fonction logarithme est strictement 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 fonction logarithme népérien (et toute fonction logarithme de base \u003E 1) est strictement croissante sur ]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":30949,"question":"Quelle est la valeur de log₂(8) ?","option_a":"2","option_b":"3","option_c":"4","option_d":"8","option_e":"","option_f":"","bonne_reponse":"b","explication":"log₂(8) = 3 car 2³ = 8. Le logarithme de 8 en base 2 est donc 3.","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\": \"3\", \"c\": \"4\", \"d\": \"8\"}}","_debug_options_count":4}]