# How do you solve 5^-x = 250?

Oct 24, 2015

$x = - {\log}_{5} \left(250\right)$

#### Explanation:

Since the logarithm is the inverse function of the exponential (i.e., ${\log}_{a} \left({a}^{x}\right) = x$, you can use ${\log}_{5}$ to isolate the $x$:

${5}^{- x} = 250 \setminus \implies {\log}_{5} \left({5}^{- x}\right) = {\log}_{5} \left(250\right)$,

but ${\log}_{5} \left({5}^{- x}\right) = - x$.

So, the equation becomes $- x = {\log}_{5} \left(250\right)$, which we easily solve for $x$ changing the sign.