SOLUTION: Solve {{{(9/16)^(2-x)=(64/27)^x

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Question 1114110: Solve Solve+(9/16)^(2-x)=(64/27)^x
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Note that 9%2F16+=+%283%2F4%29%5E2 and 64%2F27+=+%284%2F3%29%5E3.

To solve the equation, we want to make the fractions the same. So rewrite %284%2F3%29%5E3 as %283%2F4%29%5E%28-3%29.

Then

%289%2F16%29%5E%282-x%29=%2864%2F27%29%5Ex
%28%283%2F4%29%5E2%29%5E%282-x%29+=+%28%28%283%2F4%29%5E-3%29%5Ex%29%29
%283%2F4%29%5E%284-2x%29+=+%283%2F4%29%5E%28-3x%29
4-2x+=+-3x
x+=+-4