# What is the inverse of y= - log_5 (-x) ?

Dec 1, 2015

${f}^{-} 1 = - {5}^{-} x$

#### Explanation:

$y = - {\log}_{5} \left(- x\right)$
Multiplying both side with the same number:
$\implies - 1 \cdot y = - 1 \cdot - {\log}_{5} \left(- x\right)$
$\implies {\log}_{5} \left(- x\right) = - y$
$\implies {5}^{{\log}_{5} \left(- x\right)} = {5}^{-} y$ (it is a rule of logarithm)
$\implies - x = {5}^{-} y$
Multiplying both side with the same number:
$\implies - 1 \cdot - x = - 1 \cdot {5}^{-} y$
$\implies x = - {5}^{-} y$
$\implies {f}^{-} 1 = - {5}^{-} x$