SOLUTION: (1/5)^2x=625, solve for x

Algebra ->  Algebra  -> Exponential-and-logarithmic-functions -> SOLUTION: (1/5)^2x=625, solve for x      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 201772: (1/5)^2x=625, solve for x
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
%281%2F5%29%5E%282x%29+=+625 Substitute 625+=+5%5E4
%281%2F5%29%5E%282x%29+=+5%5E4 Substitute 5%5E4+=+%281%2F5%29%5E-4
%281%2F5%29%5E%282x%29+=+%281%2F5%29%5E-4 If the bases (1%2F5) are equal, the exponents are equal, so...
2x+=+-4 Divide both sides by 2.
highlight%28x+=+-2%29
Check:
%281%2F5%29%5E%282x%29+=+625 Substitute x = -2.
%281%2F5%29%5E-4+=+625
5%5E4+=+625
625+=+625 OK!