# How do you solve 2^(3x-1) = 4^(x+2)?

Hi there!

To solve this problem, you'll need to bring some exponent laws into play!

#### Explanation:

To solve a problem involving exponential equations, the first thing you want to try is to get the exponentials to the same smallest base by using an exponent.

Between 2 and 4, can you get this down to the same base? Sure! You can get the 4 down to a 2 and squaring like so:

${2}^{3 x - 1} = {\left({2}^{2}\right)}^{x + 2}$

Now use distributive property on the right hand side:

${2}^{3 x - 1} = {2}^{2 x + 4}$

Now because you have equations with the same base, you can drop the basses leaving this:

$3 x - 1 = 2 x + 4$

This is an easy equation to solve! Rearranging and combining like terms we get:

$x = 5$

And that's it! Hopefully that helps you out! If you have any questions or need some clarification, please feel free to leave a comment! :)