SOLUTION: Write expression as sum/difference of logarithms. Express as powers of factors: log (sub 2) (a^2 square root of b)^4, a>0, b>0. I got this far: log sub 2 a^8 + log sub 2 (squa

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Question 203466This question is from textbook Sullivan College Algebra
: Write expression as sum/difference of logarithms. Express as powers of factors: log (sub 2) (a^2 square root of b)^4, a>0, b>0.
I got this far: log sub 2 a^8 + log sub 2 (square root of b)^4
but I'm not even so sure about that. Can you pls show me how to finish? THanks!
This question is from textbook Sullivan College Algebra

Answer by jsmallt9(2063) About Me  (Show Source):
You can put this solution on YOUR website!
log%282%2C+%28a%5E2%2Asqrt%28b%29%29%5E4%29
log%282%2C+%28a%5E8%29%29+%2B+log%282%2C+%28sqrt%28b%29%5E4%29%29
Is good so far. We can simplify the 2nd log by using the fact that a square root is the same as an exponent of 1/2:
log%282%2C+%28a%5E8%29%29+%2B+log%282%2C+%28%28b%5E%281%2F2%29%29%5E4%29%29
log%282%2C+%28a%5E8%29%29+%2B+log%282%2C+%28b%5E2%29%29
This is a sum of logarithms. I'm not sure what "Express as powers of factors" means. But I am guessing that the next simplification is desired. We can use the following property of logarithms: log%28%28x%5Ey%29%29+=+y%2Alog%28x%29. This allows us to "move" an exponent from the argument "out in front":
8log%282%2C+%28a%29%29+%2B+2log%282%2C+%28b%29%29