# How do you solve 4^(x-3)=1/16?

Sep 10, 2016

$x = 1$

#### Explanation:

There are 2 approaches which I use for exponential equations, which are equations which have indices.

$\rightarrow$ make the bases the same
$\rightarrow$ make the indices the same

If neither of these work, then use logs.

We should know that 16 is a power of 4, so use 4 as the base on both sides.

${4}^{x - 3} = \frac{1}{16} = \frac{1}{4} ^ 2$

${4}^{x - 3} = {4}^{-} 2 \text{ } \leftarrow$ now equate the indices

$x - 3 = - 2$

$x = - 2 + 3 = 1$