Quiz : Maîtrisez les logarithmes en 10 questions

Question 1 sur 10 10:00

[{"id":27238,"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, car 10² = 100.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27239,"question":"La fonction logarithme népérien ln(x) est définie pour x \u003E 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction ln(x) est bien définie uniquement pour x \u003E 0, car le logarithme d'un nombre négatif ou nul n'existe pas dans les réels.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27240,"question":"Quelle propriété est correcte pour ln(a×b) ?","option_a":"ln(a) + ln(b)","option_b":"ln(a) × ln(b)","option_c":"ln(a) - ln(b)","option_d":"ln(a) \/ ln(b)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La propriété fondamentale est ln(a×b) = ln(a) + ln(b), valable pour a \u003E 0 et b \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27241,"question":"L'équation ln(x) = 2 admet pour solution x = e².","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En appliquant l'exponentielle des deux côtés, on obtient x = e², car ln(x) = 2 ⇔ x = e².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27242,"question":"Quelle est la dérivée de la fonction f(x) = ln(3x) ?","option_a":"1\/x","option_b":"3\/x","option_c":"1\/(3x)","option_d":"3","option_e":"","option_f":"","bonne_reponse":"C","explication":"La dérivée de ln(3x) est (1\/(3x)) × 3 = 1\/x, car la dérivée de ln(u) est u'\/u.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27243,"question":"L'inéquation ln(x) \u003C 0 est équivalente à x \u003C 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"ln(x) \u003C 0 ⇔ x \u003C 1, car ln(1) = 0 et la fonction ln est croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27244,"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) = log₂(2³) = 3, car 2³ = 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27245,"question":"La fonction ln(x) est-elle 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 ln(x) est strictement croissante sur ]0, +∞[, car sa dérivée 1\/x est toujours positive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27246,"question":"Quelle propriété est correcte pour logₐ(bⁿ) ?","option_a":"n × logₐ(b)","option_b":"logₐ(b) + n","option_c":"logₐ(b) \/ n","option_d":"(logₐ(b))ⁿ","option_e":"","option_f":"","bonne_reponse":"A","explication":"La propriété est logₐ(bⁿ) = n × logₐ(b), valable pour a \u003E 0, a ≠ 1 et b \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27247,"question":"L'équation log₁₀(x) = -1 admet pour solution x = 0,1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"log₁₀(x) = -1 ⇔ x = 10⁻¹ = 0,1, car 10⁻¹ = 0,1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]