Question

Sabendo - se que logx a =8, logx b=2 e logx c=1, calcular:

LOGX RAIZ 3 AB / C =

Answer 1

$Sabe-se\ que:\\ \\ \large\boxed{log_b~\frac{a}{c}=log_b~a-log_b~c}}\\ \\ Por\ isso,\ temos\ que:\\ \\ K = log_x~\frac{\sqrt{3}(a\cdot~b)}{c}\\ \\ K = log_x~\sqrt{3}\cdot~a+log_x\sqrt{3}\cdot~b - log_x~c\\ \\ K=\sqrt{3}\cdot~8+\sqrt{3}\cdot~2-1\\ \\ K = 8\sqrt{3}+2\sqrt{3}-1\\ \\ \large\boxed{K = 10\sqrt{3}-1}}$