How do you write the equivalent logarithmic equation $e^{- x} = 5$ $e^-x=5$ ?

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Answer 1 · 2018-03-08T14:24:14

$- x = ln 5$ $-x=ln5$

We start with

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

Take the logarithm on both sides

${ln e}^{- x} = ln 5$ $lne^-x=ln5$

Use the identity ${ln a}^{b} = b ln a$ $lna^b=blna$

$- x ln e = ln 5$ $-xlne=ln5$

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

$- x = ln 5$ $-x=ln5$

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