# How do you solve ln x = -3 ?

$x = \frac{1}{e} ^ 3$

#### Explanation:

Given that

$\setminus \ln x = - 3$

${e}^{\setminus \ln x} = {e}^{- 3} \setminus \quad \left(\setminus \textrm{r a i \sin g p o w e r s \to b a s e e}\right)$

$x = {e}^{- 3}$

$x = \frac{1}{e} ^ 3$

Jul 19, 2018

$x = \frac{1}{e} ^ 3$

#### Explanation:

We want to cancel out the natural log function. To go about doing this, we can apply its inverse, base $e$ to both sides. We get

${e}^{\ln} x = {e}^{-} 3$

This simplifies to

$x = \frac{1}{e} ^ 3$

As a decimal, this is approximately $0.04979$

Hope this helps!