# How do you write the equivalent logarithmic equation e^-x=5?

Mar 8, 2018

#### Answer:

$- x = \ln 5$

#### Explanation:

We start with

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

Take the logarithm on both sides

$\ln {e}^{-} x = \ln 5$

Use the identity $\ln {a}^{b} = b \ln a$

$- x \ln e = \ln 5$

Use the fact that $\ln e = 1$ to simplify

$- x = \ln 5$