SOLUTION: How would I find x? My problem is (1/4)^(x-1)=32^(x+3). I've tried plugging in numbers but my teacher showed us a formula I think but I never understood it.

Question 329560: How would I find x? My problem is (1/4)^(x-1)=32^(x+3). I've tried plugging in numbers but my teacher showed us a formula I think but I never understood it.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
How would I find x? My problem is (1/4)^(x-1)=32^(x+3). I've tried plugging in numbers but my teacher showed us a formula I think but I never understood it.
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(1/4)^(x-1)=32^(x+3)
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Change both sides to a common base as follows:
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[(2^-2)^(x-1)] = [(2^5)^(x+3)]
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2^(-2x+2) = 2^(5x+15)
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Equate the exponents:
-2x+2 = 5x+15
7x = -13
x = -13/7
===============
Cheers,
Stan H.

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