Testez vos connaissances sur les logarithmes — Bac Math

Question 1 sur 10 10:00

[{"id":78612,"question":"Quelle est la valeur de log(1) ?","option_a":"0","option_b":"1","option_c":"10","option_d":"-1","option_e":"","option_f":"","bonne_reponse":"A","explication":"log(1) = 0 car 10^0 = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78613,"question":"La fonction logarithme 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 fonction logarithme est strictement croissante sur ]0, +∞[.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78614,"question":"Quelle est la dérivée de la fonction f(x) = ln(x) ?","option_a":"1\/x","option_b":"x","option_c":"ln(x)","option_d":"e^x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de ln(x) est 1\/x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78615,"question":"L'égalité log(a) + log(b) = log(a + b) est-elle toujours vraie ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'égalité correcte est log(a) + log(b) = log(a*b).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78616,"question":"Quelle est la solution de l'équation ln(x) = 2 ?","option_a":"x = 2","option_b":"x = e^2","option_c":"x = ln(2)","option_d":"x = 10^2","option_e":"","option_f":"","bonne_reponse":"B","explication":"ln(x) = 2 ⇒ x = e^2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78617,"question":"La fonction logarithme est-elle définie pour x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction logarithme n'est pas définie pour x ≤ 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78618,"question":"Quelle propriété permet d'écrire ln(a^n) = n*ln(a) ?","option_a":"Propriété de l'exposant","option_b":"Propriété du logarithme d'un produit","option_c":"Propriété du logarithme d'une puissance","option_d":"Propriété de la dérivée","option_e":"","option_f":"","bonne_reponse":"C","explication":"C'est la propriété du logarithme d'une puissance : ln(a^n) = n*ln(a).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78619,"question":"L'équation ln(x) = ln(y) implique-t-elle x = y ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Oui, car la fonction logarithme est injective (strictement croissante).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78620,"question":"Quelle est la valeur de log(100) ?","option_a":"1","option_b":"2","option_c":"10","option_d":"100","option_e":"","option_f":"","bonne_reponse":"B","explication":"log(100) = 2 car 10^2 = 100.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78621,"question":"La fonction logarithme est-elle définie pour x = -1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Non, car x doit être strictement positif.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]