# How do you solve log(x-5)=-2?

Jun 6, 2016

Applying the exponential on both sides.

#### Explanation:

Your $x$ is in the $\log$, so you have to remove it. The inverse operation of the $\log$ is the exponential, so you can do

$\log \left(x - 5\right) = - 2$

${e}^{\log \left(x - 5\right)} = {e}^{-} 2$

Because, as said, the exponential is the inverse of the logarithm, we have

$x - 5 = {e}^{-} 2$

and finally

$x = {e}^{-} 2 + 5 \setminus \approx 5.13$