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

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#### Explanation

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#### Explanation:

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Mar 8, 2018

$- x = \ln 5$

#### Explanation:

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

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

$- x = \ln 5$

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