# How do you solve ln 2x = -8?

Aug 6, 2015

$x = \frac{{e}^{- 8}}{2} \approx 1.7 \cdot {10}^{- 4}$

#### Explanation:

The relationship between the logartihm and exponential functions is:

$\ln \left(x\right) = y \leftrightarrow {e}^{y} = x$

Therefore:

$\ln \left(2 x\right) = - 8 \rightarrow 2 x = {e}^{- 8} \rightarrow x = \frac{{e}^{- 8}}{2} \approx 1.7 \cdot {10}^{- 4}$