SOLUTION: Please help me solve this equation: 4^xsquared/4^2x=64

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Question 319938: Please help me solve this equation: 4^xsquared/4^2x=64
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!


Subtract exponents of 4 on the left:

drawing%28100%2C130%2C-1%2C1%2C-1%2C.5%2C+locate%28-1%2C0%2C+4%5E%28x%5E2-2x%29=64%29+++%29

Since 4*4*4 = 64 write 64 as 4%5E3



equate the exponents of 4 on each side:

x%5E2-2x=3

x%5E2-2x-3=0

%28x-3%29%28x%2B1%29=0

    

Two solutions 3 and -1

Checking x=3



drawing%28100%2C130%2C-1%2C1%2C-1%2C.5%2C+locate%28-1%2C0%2C+4%5E9%2F4%5E6=64%29+%29++
4%5E3=64
64=64

Checking x=-1




4%5E%281-%28-2%29%29=64%29+%29++
4%5E%281%2B2%29=64
4%5E3=64
64=64

So both solutions check.

Edwin