# How do you solve 5^-x = 3?

Jun 3, 2016

Using the log.

#### Explanation:

To solve the equations where the $x$ is in the exponent, the trick is to do the logarithms.

${5}^{- x} = 3$

$\log \left({5}^{- x}\right) = \log \left(3\right)$

we then apply the property of the logarithm where the exponent in the log goes in front multiplying.

$- x \log \left(5\right) = \log \left(3\right)$

$x = - \log \frac{3}{\log} \left(5\right) \setminus \approx - 0.68$.