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!

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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)   (Show Source): You can put this solution on YOUR website!
Just use the fact that . Here, we have

. The exponents must be equal, so we set 4x+2 equal to 2x-2 and solve.



.
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
3^(4x+2) =9^(x-1)
---
3^(4x+2) = (3^2)^(x-1)
---
3^(4x+2) = 3^(2x-2)
---
4x+2 = 2x-2
2x = -4
x = -2
=========
Cheers,
Stan H.
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!


Hi

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

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

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 

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