How to solve an equation by expressing each side as a power of the same base and then equating exponents

Question

4^(3x-7)=16

Answer 1

4^(3x-7) = 4^2

 

3x-7 = 2

 

3x = 9

 

 x=3

 

Check:   4^ (3*3-7) = 4 ^ ( 9-7) = 4^2 = 16

Answer 2

Edited solution in the Comments box. I was unable to edit a typo in the Answer box.