# How do you solve for x in 9^x=1/81?

Dec 4, 2015

$x = - 2$

#### Explanation:

First of all, observe that ${9}^{2} = 81$. Then, remember how negative powers work:

${a}^{- b} = \frac{1}{a} ^ \left\{b\right\}$.

So, we have that $\frac{1}{81} = \frac{1}{9} ^ 2 = {9}^{- 2}$.

Now, we know that ${9}^{x} = {9}^{- 2}$.

And so $x = - 2$.