SOLUTION: How do you solve this equation: 5 to pwer x x 3 power y = 675 Thank you!

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Question 1072157: How do you solve this equation:
5 to pwer x x 3 power y = 675
Thank you!
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
How do you solve this equation:
5 to pwer x x 3 power y = 675
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I assume the equation to be solved is +%285%5Ex%29%283%5Ey%29+=+675+ and you want to solve for y.
+log%28%285%5Ex%2A3%5Ey%29%29+=+log%28%28675%29%29+
Use log(A*B) = log(A)+log(B) on left side, and take log of right (I'm using ln() for log()):
++log%28%285%5Ex%29%29%2Blog%28%283%5Ey%29%29+=+6.5147127++
Use this fact log%28%28z%5Ek%29%29+=+k%2Alog%28%28z%29%29+ to rewrite left side:
++++x%2Alog%285%29+%2B+y%2Alog%283%29+=+6.5147127+
Solve for y:
++++y+=+%286.5147127+-+x%2Alog%28%285%29%29%29+%2F+log%28%283%29%29+
+++y+=+highlight%28+5.9299470+-+1.46497352%2Ax+%29