SOLUTION: If {{{16^x=2^(x+5)-2^(x+4)}}}, what is the value of {{{x}}}?

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Question 1114458: If 16%5Ex=2%5E%28x%2B5%29-2%5E%28x%2B4%29, what is the value of x?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
16%5Ex = 2%5E%28x%2B5%29-2%5E%28x%2B4%29   is the same as


16%5Ex = 2%5E%28x%2B4%29%2A%282-1%29    is the same as


16%5Ex = 2%5E%28x%2B4%29   is the same as


2%5E%284x%29 = 2%5E%28x%2B4%29,   which implies


4x = x+4   ====>  3x = 4  ====>  x = 4%2F3.

Solved.