# What is the inverse of y=log(4x) ?

Nov 13, 2015

$x = {e}^{y} / 4$

#### Explanation:

We must find a relation of the form $x = f \left(y\right)$. To do so, observe that, since exponential and logarithms are inverse one of the other, we have that ${e}^{\log \left(x\right)} = x$. So, taking the exponential at both sizes, we have

${e}^{y} = {e}^{\log \left(4 x\right)}$, which means

${e}^{y} = 4 x$, and finally

$x = {e}^{y} / 4$