SOLUTION: Solve Simultaneously for x and y: 4^x(times)2^y=16 and 8^x=2^(y/2)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Solve Simultaneously for x and y: 4^x(times)2^y=16 and 8^x=2^(y/2)      Log On


   

Question 386514: Solve Simultaneously for x and y:
4^x(times)2^y=16
and
8^x=2^(y/2)
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi, You are absolutely correct 

4^x (2^y)=16

(2^2x)(2^y) = 2^4

In general, %28x%5Em%29%28x%5En%29+=+x%5E%28m%2Bn%29

 2^(2x+y) = 2^4      both sides of equation with the same base

    +2x+%2B+y+=+4+  Exponents are also equal



8^x= 2^(y/2)

 2^3x = 2^(y/2)

   3x = y/2

   6x = y



   2x + y = 4

   2x + 6x = 4  Substituting  6x for y

       8x = 4  

        x = 1/2   y = 3   (6*(1/2)