# How do you solve ln (1/e^5)=x?

Jul 22, 2016

The soln. is  : x=-5

#### Explanation:

$\ln \left(\frac{1}{e} ^ 5\right) = x$

We know that, $\frac{1}{e} ^ a = {e}^{- a} , \mathmr{and} , \ln {e}^{b} = b$

:. ln(e^(-5))=ln (e^x))............(1)#

Now, $\ln$ fun. is $1 - 1$. Hence, $\left(1\right) \Rightarrow {e}^{- 5} = {e}^{x}$.

Again, fun. ${e}^{x}$ is $1 - 1$, so, $x = - 5$ is the soln.