SOLUTION: Solve 3^x-1= 9^2x

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Question 199620: Solve 3^x-1= 9^2x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3%5E%28x-1%29=9%5E%282x%29 Start with the given equation.


3%5E%28x-1%29=%283%5E2%29%5E%282x%29 Rewrite 9 as 3%5E2


3%5E%28x-1%29=3%5E%282%282x%29%29 Multiply the exponents


3%5E%28x-1%29=3%5E%284x%29 Multiply


x-1=4x Since the bases are equal, the exponents are equal.


x=4x%2B1 Add 1 to both sides.


x-4x=1 Subtract 4x from both sides.


-3x=1 Combine like terms on the left side.


x=%281%29%2F%28-3%29 Divide both sides by -3 to isolate x.


x=-1%2F3 Reduce.


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Answer:

So the solution is x=-1%2F3 which approximates to x=-0.333.