# How do you solve -5e^(-x)+9=6?

Sep 6, 2016

$x = - \ln \left(\frac{3}{5}\right)$

#### Explanation:

We have: $- 5 {e}^{- x} + 9 = 6$

Let's begin by subtracting $9$ from both sides of the equation:

$\implies - 5 {e}^{- x} = - 3$

Then, let's divide both sides by $- 5$:

$\implies {e}^{- x} = \frac{3}{5}$

Now, let's apply the natural logarithm to both sides:

$\implies \ln \left({e}^{- x}\right) = \ln \left(\frac{3}{5}\right)$

Using the laws of logarithms:

$\implies - x \ln \left(e\right) = \ln \left(\frac{3}{5}\right)$

$\implies - x \cdot 1 = \ln \left(\frac{3}{5}\right)$

$\implies - x = \ln \left(\frac{3}{5}\right)$

Finally, to solve for $x$, let's divide both sides by $- 1$:

$\implies x = - \ln \left(\frac{3}{5}\right)$