Les fonctions logarithmes : propriétés, équations et dérivées

Question 1 sur 5 10:00

[{"id":2310,"question":"Quelle est la valeur de ln(e^3) ?","option_a":"3","option_b":"e^3","option_c":"0","option_d":"1","option_e":"","option_f":"","bonne_reponse":"A","explication":"ln(e^3) = 3·ln(e) = 3·1 = 3, car ln(e) = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":2311,"question":"Quelle est la solution de l'équation ln(x) = 2 ?","option_a":"x = e^2","option_b":"x = 2","option_c":"x = ln(2)","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"En appliquant la fonction exponentielle des deux côtés, on obtient x = e^2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":2312,"question":"Quelle est la dérivée de f(x) = ln(2x + 1) ?","option_a":"f'(x) = 1\/(2x + 1)","option_b":"f'(x) = 2\/(2x + 1)","option_c":"f'(x) = 2x\/(2x + 1)","option_d":"f'(x) = 1\/x","option_e":"","option_f":"","bonne_reponse":"B","explication":"En utilisant la règle de la chaîne, f'(x) = (1\/(2x + 1)) · 2 = 2\/(2x + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":2313,"question":"Quelle est la valeur de log_10(1000) ?","option_a":"3","option_b":"100","option_c":"10","option_d":"0","option_e":"","option_f":"","bonne_reponse":"A","explication":"log_10(1000) = log_10(10^3) = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":2314,"question":"Quelle est la limite de ln(x) lorsque x tend vers 0+ ?","option_a":"0","option_b":"-∞","option_c":"+∞","option_d":"1","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction ln(x) tend vers -∞ lorsque x tend vers 0 par la droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]