# How do you solve 4.12=e^(-2x)?

Jul 11, 2016

$x = - 0.71$ to 2dp

#### Explanation:

$4.12 = {e}^{- 2 x}$

Taking natural log of both sides

$\ln \left(4.12\right) = \ln {e}^{- 2 x}$

Can rewrite using rules of logs as

$\ln \left(4.12\right) = - 2 x \ln e$

ln and exp are inverse operations so cancel out:

$\ln \left(4.12\right) = - 2 x \implies x = - \frac{1}{2} \ln \left(4.12\right)$

$\therefore x = - 0.71$ to 2dp