Hi

solving:

  4^2x = 32^1/2



 ( 2^2)^2x = (2^5)^1/2

    2^4x = 2^5/2

      4x = 5/2

       x = 5/8

CHECKING our Answer***

 4^(2*5/8)= 4^5/4  = 2^10/4 = 2^5/2 

Answer by Coyote 10(7)   (Show Source): You can put this solution on YOUR website!
 First Convert 2^4x to (2^2)^2x and convert 32^1/2 to (2^5)(1/2). distribute 2x to the (2^2) to yield 2^4x and distribute 1/2 to 2^5 to yield 2^5/2. Thus your problem would become 2^4x=2^5/2. Because you have common bases you can simplify your problem to 4x=5/2. divide both sides by four and your answer would be 5/8 

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