SOLUTION: Determine all values of x for which {{{ (2*4^(x^2-3x))^2= 2^(x-1)}}}

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Question 1114887: Determine all values of x for which +%282%2A4%5E%28x%5E2-3x%29%29%5E2=+2%5E%28x-1%29
Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


+%282%2A4%5E%28x%5E2-3x%29%29%5E2=+2%5E%28x-1%29

Rewrite every factor as a power of 2; then equate the exponents.

%282%2A%282%5E2%29%5E%28x%5E2-3x%29%29%5E2+=+2%5E%28x-1%29
%282%5E2%29%2A2%5E%284x%5E2-12x%29+=+2%5E%28x-1%29
2%5E%284x%5E2-12x%2B2%29+=+2%5E%28x-1%29
4x%5E2-12x%2B2+=+x-1
4x%5E2-13x%2B3+=+0
%284x-1%29%28x-3%29+=+0
x+=+1%2F4 or x+=+3

Answers: x=1/4 and x=3