SOLUTION: Solve for x: {{{3^(-x)=(1/9)^(x+1)}}}

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Question 140337: Solve for x: 3%5E%28-x%29=%281%2F9%29%5E%28x%2B1%29
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3%5E%28-x%29=%281%2F9%29%5E%28x%2B1%29 Start with the given equation


3%5E%28-x%29=%281%2F3%5E2%29%5E%28x%2B1%29 Rewrite 9 as 3%5E2


1%2F3%5E%28x%29=%281%2F3%5E2%29%5E%28x%2B1%29 Rewrite 3%5E%28-x%29 as 1%2F3%5E%28x%29


1%2F3%5E%28x%29=%281%2F3%5E%282%28x%2B1%29%29%29 Distribute the exponent on the right side


3%5E%28x%29=3%5E%282%28x%2B1%29%29 Flip both fractions


Since the bases are equal, this means that the exponents are equal


So x=2%28x%2B1%29



x=2x%2B2 Distribute


x-2x=2 Subtract 2x from both sides


-x=2 Combine like terms on the left side


x=%282%29%2F%28-1%29 Divide both sides by -1 to isolate x



x=-2 Divide

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Answer:
So our answer is x=-2