Testez vos connaissances sur la fonction logarithmique — Terminale Math

Question 1 sur 10 10:00

[{"id":77512,"question":"Quelle est la dérivée de la fonction f(x) = ln(x) ?","option_a":"A. 1\/x","option_b":"B. x","option_c":"C. e^x","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de ln(x) est 1\/x, une propriété fondamentale à retenir.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77513,"question":"L'équation ln(x) = 0 admet-elle une solution ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"ln(1) = 0, donc l'équation admet une solution unique x = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77514,"question":"Quelle est la valeur de ln(e^3) ?","option_a":"A. 3","option_b":"B. e","option_c":"C. 1\/3","option_d":"D. 0","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":77515,"question":"La fonction ln(x) est-elle définie pour x = -1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction ln(x) n'est définie que pour x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77516,"question":"Quelle propriété permet d'écrire ln(ab) = ln(a) + ln(b) ?","option_a":"A. Propriété de linéarité","option_b":"B. Propriété multiplicative","option_c":"C. Propriété additive","option_d":"D. Propriété exponentielle","option_e":"","option_f":"","bonne_reponse":"C","explication":"C'est la propriété additive des logarithmes, valable pour a \u003E 0 et b \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77517,"question":"Si ln(x) = 2, quelle est la valeur de x ?","option_a":"A. 2","option_b":"B. e^2","option_c":"C. 1\/2","option_d":"D. ln(2)","option_e":"","option_f":"","bonne_reponse":"B","explication":"ln(x) = 2 ⇒ x = e^2, car ln(e^2) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77518,"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 dérivée de ln(x) est 1\/x \u003E 0 pour x \u003E 0, donc la fonction est strictement croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77519,"question":"Quelle est la limite de ln(x) lorsque x tend vers 0+ ?","option_a":"A. 0","option_b":"B. -∞","option_c":"C. +∞","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"B","explication":"Lorsque x → 0+, ln(x) → -∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77520,"question":"Si ln(a) = ln(b), peut-on conclure que a = b ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Oui, car la fonction ln est injective (strictement croissante) sur son ensemble de définition.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77521,"question":"Quelle est la solution de l'équation ln(x+1) = 2 ?","option_a":"A. x = e^2 - 1","option_b":"B. x = e^2 + 1","option_c":"C. x = 2","option_d":"D. x = 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"ln(x+1) = 2 ⇒ x+1 = e^2 ⇒ x = e^2 - 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]