Question

CALCULE O VALOR DO LOGARITMO

Answer 1

a)
     Seja x o logaritmo
           $log(4) \sqrt[8]{16} =x \\ \\ 16^{ \frac{1}{8} } =4^x \\ \\ (2^4) ^{ \frac{1}{8} } =(2^2)^x \\ \\ 2^{ \frac{1}{2} } =2^{2x} \\ \\ \frac{1}{2} =2x \\ \\ x= \frac{1}{4}$

b)
     Seja y o logaritmo
           $log(9)81=y \\ \\ 81=9^y \\ \\ 3^4=(3^2)^y \\ \\ 4=2y \\ \\ y= \frac{4}{2} \\ \\ y=2$

Answer 2

$a)~~log_4~ \sqrt[8]{16} \to~~ \sqrt[8]{16}=4^x \to~~ 16^{ \frac{1}{8} }=4^x\to~~ \not4^{2. \frac{1}{8} }=\not4^x\to\\\\ 2. \dfrac{1}{8} =x\to~~ x= \dfrac{2}{8} \to~~ \boxed{x= \dfrac{1}{4} }$




$b)~~ log_9~81\to~~81=9^x\to~~\not9^2=\not9^x\to~~ \boxed{x=2}$