Question

log de 4 na base 1/4

Answer 1

$log_{(\frac{1}{4})}4=x$

Aplicando a definição de logaritmos: $\boxed{base^{logaritmo}=logaritmando}$

$(\frac{1}{4})^{x}=4\\\\(\frac{1}{4})^{x}=(\frac{1}{4})^{-1}$

Bases iguais, iguale os expoentes:

$x=-1~~~~~~\therefore~~~~~~\boxed{\boxed{log_{(\frac{1}{4})}4=-1}}$

Answer 2

log    4
    1/4
(1/4)^x = 4
(1/2²)^x = 2^2
(2⁻ ²)^x = 2^2
2^(- 2x) = 2^2
- 2x = 2 . (- 1)
2x = - 2
x = - 2/2
x = - 1