SOLUTION: (Capital X's are variables, small x's are multiplication symbols) Hi, I was asked to solve this question: 16^(X-5) = 32^(1/3X) + 2 I first did this: 16^X / 16^5 = 32^1/3X x 32^

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Question 375400: (Capital X's are variables, small x's are multiplication symbols)
Hi, I was asked to solve this question: 16^(X-5) = 32^(1/3X) + 2
I first did this: 16^X / 16^5 = 32^1/3X x 32^2
Then: 16^X / 32^1/3X = 16^5 + (16^2 x 4)
I'm not sure where to go from here, I have the answer (from the sheet) but I really want to know how to do it for future reference. Thanks!!
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
I first did this: 16^X / 16^5 = 32^1/3X x 32^2
Then: 16^X / 32^1/3X = 16^5 + (16^2 x 4)
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Use the asterisk for multiply, *
Everyone does.
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16^x/16^5 = 32^(x/3)*32^2
16^(x-5) = 32^(x/3 + 2)
Change bases to 2, since 16 = 2^4 and 32 = 2^5
2^(4x-20) = 2^(5x/3 + 10)
4x-20 = (5/3)x + 10
(7/3)x = 30
x = 90/7