SOLUTION: 2^(log(base4)x) My book says the answer is sqrt(x). Any explanation would be great.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 2^(log(base4)x) My book says the answer is sqrt(x). Any explanation would be great.      Log On


   

Question 1151658: 2^(log(base4)x)
My book says the answer is sqrt(x). Any explanation would be great.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!


+y+=+2%5E%28log%284%2C%28x%29%29%29+



Take log_2 both sides:

+log%282%2C%28y%29%29+=+log%284%2C%28x%29%29+



Raise 4 to both sides:

+4%5E%28log%282%2C%28y%29%29%29+=+x+



Re-write left hand side:

+2%5E%282%28log%282%2C%28y%29%29%29%29+=+x+

+y%5E2+=+x+

+y+=+sqrt%28x%29+