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

1 Answer

Hi there!

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


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^(3x-1) = (2^2)^(x+2)#

Now use distributive property on the right hand side:

# 2^(3x-1) = 2^(2x+4)#

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

#3x-1 = 2x +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! :)