SOLUTION: Please help me answer this: 3^(4x) = 27^(x-2) Thanks.

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Question 199666: Please help me answer this:
3^(4x) = 27^(x-2)
Thanks.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3%5E%284x%29+=+27%5E%28x-2%29 Start with the given equation.


3%5E%284x%29+=+%283%5E3%29%5E%28x-2%29 Rewrite 27 as 3%5E3


3%5E%284x%29+=+3%5E%283%28x-2%29%29 Multiply the exponents.


4x+=+3%28x-2%29 Since the bases are equal, the exponents are equal.


4x=3x-6 Distribute.


4x-3x=-6 Subtract 3x from both sides.


x=-6 Combine like terms on the left side.


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Answer:

So the solution is x=-6