SOLUTION: 25^(log(base5)(3x^2)) Is the answer 9x^4? If not can you show the the steps?

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 25^(log(base5)(3x^2)) Is the answer 9x^4? If not can you show the the steps?      Log On


   

Question 1151694: 25^(log(base5)(3x^2))
Is the answer 9x^4? If not can you show the the steps?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


25%5E%28log%285%2C3x%5E2%29%29

The problem involves logs base 5; 25 is a power of 5, so write 25 as a power of 5.

%285%5E2%29%5E%28log%285%2C3x%5E2%29%29

Use the exponent rule %28a%5Eb%29%5Ec+=+a%5E%28bc%29+=+%28a%5Ec%29%5Eb...
5%5E%28%28log%285%2C3x%5E2%29%29%29%5E2

Use the rule a%5Elog%28a%2Cb%29+=+b...
%283x%5E2%29%5E2

And now it's just basic algebra

9x%5E4

Your answer is right....