SOLUTION: Solve: 9^(3x-1)=81^(-x+1)

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Question 122246: Solve: 9^(3x-1)=81^(-x+1)
Answer by Fombitz(13828) About Me  (Show Source):
You can put this solution on YOUR website!
9%5E%283x-1%29=81%5E%28-x%2B1%29
9%5E%283x-1%29=%289%5E2%29%5E%28-x%2B1%29 Substitute for 81.
9%5E%283x-1%29=%289%5E%282%2A%28-x%2B1%29%29%29 Rule for multiplying exponents.
%283x-1%29=2%2A%28-x%2B1%29 Take log base 9 of each side.
3x-1=-2x%2B2
5x=3
x=3%2F5
Check your answer.
9%5E%283x-1%29=81%5E%28-x%2B1%29
9%5E%283%283%2F5%29-1%29=81%5E%28%28-3%2F5%29%2B1%29
9%5E%289%2F5-5%2F5%29=81%5E%282%2F5%29
9%5E%284%2F5%29=81%5E%282%2F5%29
5.80=5.80