SOLUTION: Solve for x: 9^(2x-1)=(1/3)^x

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Question 1056039: Solve for x: 9^(2x-1)=(1/3)^x
Found 2 solutions by Alan3354, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x: 9^(2x-1)=(1/3)^x
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(2x-1)*log(9) = x*log(1/3)
2x*log(9) - log(9) = x*log(1/3)
2x*log(9) - x*log(1/3) = log(9)
x*log(81) - x*log(1/3) = log(9)
x*(log(81) - log(1/3)) = log(9)
x*log(243) = log(9)
x = log(9)/log(243) = 2log(3)/(5log(3))
x = 2/5

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Solve for x: 9^(2x-1)=(1/3)^x
9%5E%282x+-+1%29+=+%281%2F3%29x

%283%5E2%29%5E%282x+-+1%29+=+%283%5E-1%29%5Ex ----- Converting matrix%281%2C7%2C+9%2C+to%2C+3%5E2%2C+and%2C+1%2F3%2C+to%2C+3%5E-+1%29

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

3%5E%284x+-+2%29+=+3%5E%28-+x%29

4x – 2 = - x ------ Bases of equation are equal and so are the exponents

4x + x = 2

5x = 2

highlight_green%28x+=+2%2F5%29