SOLUTION: I need help solving this equation. Thank you. (1/9)^x+2 = 27^x-2

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Question 887442: I need help solving this equation. Thank you.
(1/9)^x+2 = 27^x-2
Found 2 solutions by Alan3354, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
(1/9)^x+2 = 27^x-2
----------
Use logs base 3
%28x%2B2%29%2Alog%283%2C%281%2F9%29%29+=+%28x-2%29%2Alog%283%2C27%29
(x+2)*-2 = (x-2)*3
-2x-4 = 3x-6
2 = 5x
x = 2/5

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

I need help solving this equation. Thank you.
(1/9)^x+2 = 27^x-2


%281%2F9%29%5E%28x+%2B+2%29+=+27%5E%28x+-+2%29

%283%5E-2%29%5E%28x+%2B+2%29+=+%283%5E3%29%5E%28x+-+2%29 ------ Converting to similar base

3%5E%28-2%28x+%2B+2%29%29+=+3%5E%283%28x+-+2%29%29

- 2(x + 2) = 3(x - 2) ------ Bases are equal, and so are their exponents

- 2x - 4 = 3x - 6

- 2x - 3x = - 6 + 4

- 5x = - 2

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

You can do the check!! 



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