solve for x:

5 (to the power x + 3 ) minus (5 to the power x+1) =600

Factor out 5^(x + 1) from the left side of your equation. Then it'll fall right into place.

5^(x+3) - 5^(x+1) = 600

5^(x+1) (5^2 -1) = 600

5^(x+1) = 25

x + 1 = 2

x = 1

Eeseely Also Disagrees.

Edited.

jiten55 seems right to me. Substitute x=1 in and you'll see it's right.

5^{1+3}-5^{1+1}=5^4-5^2=625-25=600