SOLUTION: if ((8^x)(9^2y))=81(2^12y) what does x equal? I have no idea where to start on this one. I had trouble writing this equation, if I were to read it I would say "if eight to the

Algebra ->  Exponents -> SOLUTION: if ((8^x)(9^2y))=81(2^12y) what does x equal? I have no idea where to start on this one. I had trouble writing this equation, if I were to read it I would say "if eight to the      Log On


   

Question 418720: if ((8^x)(9^2y))=81(2^12y) what does x equal?
I have no idea where to start on this one.
I had trouble writing this equation, if I were to read it I would say "if eight to the x times nine to the two y equals 81 times two to the 12 y, what does x equal?
Thank you so much!
Found 2 solutions by Alan3354, sudhanshu_kmr:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
if ((8^x)(9^2y))=81(2^12y) what does x equal?
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You can solve for x in terms of y.
%28%288%5Ex%29%289%5E%282y%29%29%29=81%282%5E%2812y%29%29
8%5Ex+=+81%2A2%5E%2812y%29%2F%289%5E%282y%29%29
Some manipultion is possible, but "simplification" is sometimes a matter of opinion.
8%5Ex+=+81%2A2%5E%2812y%29%2F%289%5E%282y%29%29
8%5Ex+=+81%2A2%5E%2812y%29%2F%2881%5E%28y%29%29
8%5Ex+=+2%5E%2812y%29%2F%2881%5E%28y-1%29%29
x%2Alog%288%29+=+12y%2Alog%282%29+-+%28y-1%29%2Alog%2881%29
x+=+%2812y%2Alog%282%29+-+%28y-1%29%2Alog%2881%29%29%2Flog%288%29
All the logs of constants are constants, so it could be calculated to be a constant times y, x = Cy

Answer by sudhanshu_kmr(1152) About Me  (Show Source):
You can put this solution on YOUR website!

((8^x)(9^2y))=81(2^12y)
=> 2^(3x) * 3^(4y) = 3^4 * 2^(12y)
here we use only exponential value at prime numbers.
now compare exponential value....
3x = 12 y
and 4y = 4
so, after solving these two equations, y = 1 , x = 4