Logaritmos

por josuel Ter 11 Abr 2017, 21:00

Se \log {_{ab}}^{a}=4, calcule \log_{ab}^{\left ( \frac{^3\sqrt{a}}{\sqrt{b}} \right )}

RESPOSTA: 17/6

por **LPavaNNN** Ter 11 Abr 2017, 21:24

n da pra entender, log de '' '' elevado a a na base ab ?

por **Elcioschin** Ter 11 Abr 2017, 22:35

Acredito que seja:

Se log_a.b(a) = 4, calcule log_a.b(∛a/√b)

log_a.b(a) = 4 ---> Mudando a base para 10 ---> log(a)/log(a.b) = 4 --->

log(a) = 4.log(a.b) ---> log(a) = 4.log(a) + 4.log(b) ---> log(b) = - (3/4).log(a)

log_a.b(∛a/√b) = log_a.b(a^1/3/b^1/2) = log_a.b(a^1/3) - log_a.b(b^1/2) --->

log_a.b(∛a/√b) = (1/3). log_a.b(a) - (1/2). log_a.b(b) = (1/3).4 - (1/2).log(b)/log(a.b)

log_a.b(∛a/√b) = 4/3 - (1/2).log(b)/[log(a) + log(b)] --->

log_a.b(∛a/√b) = 4/3 - (1/2).[- (3/4).log(a)]/[loga) - (3/4).log(a)] --->

log_a.b(∛a/√b) = 4/3 - (1/2).[- (3/4)]/[1 - (3/4)] = 4/3 - (1/2).(- 3/4)/(1/4) --->

log_a.b(∛a/√b) = 4/3 + 3/2 = 17/6

Por favor confiram as contas.