SOLUTION: What is the answer to {{{(1/5)^(x-2) = 125^(x/2)}}} I don't understand ho w to do this problem at all. THANKS!

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: What is the answer to {{{(1/5)^(x-2) = 125^(x/2)}}} I don't understand ho w to do this problem at all. THANKS!      Log On


   

Question 256241: What is the answer to %281%2F5%29%5E%28x-2%29+=+125%5E%28x%2F2%29
I don't understand ho w to do this problem at all.
THANKS!
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
[5^(-1)]^(x-2) = (5^3)^(x/2)

5^(2-x) = 5^(3x / 2)

2 - x = 3x / 2 ___ 4 - 2x = 3x ___ 4 = 5x ___ 4/5 = x