Solve the following equation for x:

log_x$\dfrac{1}{4}$ = -1

Given,

⇒ log_x$\dfrac{1}{4}$ = -1

$\Rightarrow x^{-1} = \dfrac{1}{4} \\[1em] \Rightarrow \dfrac{1}{x} = \dfrac{1}{4} \\[1em] \Rightarrow x = 4.$

Hence, x = 4.