SOLUTION: Solve the equation 3^(4x+2) =9^(x-1) (Hint: Write both sides as a power of 3 and then match the powers.) I do not get this problem even with the hint. Please help. :) Thanks!

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Solve the equation 3^(4x+2) =9^(x-1) (Hint: Write both sides as a power of 3 and then match the powers.) I do not get this problem even with the hint. Please help. :) Thanks!      Log On


   

Question 429092: Solve the equation 3^(4x+2) =9^(x-1) (Hint: Write both sides as a power of 3 and then match the powers.)
I do not get this problem even with the hint. Please help. :) Thanks!
Found 3 solutions by richard1234, stanbon, ewatrrr:
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Just use the fact that %28a%5Eb%29%5En+=+a%5E%28bn%29. Here, we have

3%5E%284x%2B2%29+=+9%5E%28x-1%29+=+%283%5E2%29%5E%28x-1%29+=+3%5E%282x-2%29. The exponents must be equal, so we set 4x+2 equal to 2x-2 and solve.

4x%2B2+=+2x-2
2x+=+-4
x+=+-2.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
3^(4x+2) =9^(x-1)
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3^(4x+2) = (3^2)^(x-1)
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3^(4x+2) = 3^(2x-2)
---
4x+2 = 2x-2
2x = -4
x = -2
=========
Cheers,
Stan H.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

3^(4x+2) = 9^(x-1)

3^(4x+2) = (3^2)^(x-1)   | %28a%5Ep%29%5Eq+=+a%5E%28p%2Aq%29

3^(4x+2) = 3^2(x-1)

  4x+2 = 2(x-1)

   2x = -4

    x = -2

CHECKING our Answer***

 3^-6 = 9^-3

 1/3^6 = 1/9^3 = 1/729