Question

Dados log a = 5, log b =3 e log c = 2, determine o valor de log$\frac{(ab4)}{(c)}$. (alteração, o expoente 4 é somente variável b)

Answer 1

eae hEric,

use as propriedades de log..

$\boxed{log_b(ac)\Rightarrow log_b(a)+log_b(c)}\\ \boxed{log_b\left( \dfrac{a}{c}\right)\Rightarrow log_b(a)-log_b(c) }\\ \boxed{log_b(a)^c\Rightarrow c\cdot log_b(a)}$

então..

$log \left(\dfrac{ab^4}{c}\right)=log(ab^4)-log(c)\\\\ log \left(\dfrac{ab^4}{c}\right)=log(a)+log(b)^4-log(c)\\\\ log \left(\dfrac{ab^4}{c}\right)= log(a)+4\cdot log(b)-log(c)\\\\ log \left(\dfrac{ab^4}{c}\right)= 5+4\cdot3-2\\\\ log \left(\dfrac{ab^4}{c}\right)=5+12-2\\\\ \huge\boxed{\boxed{log \left(\dfrac{ab^4}{c}\right)=15}}$

Tenha ótimos estudos ;D