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

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(3758) (Show Source): You can put this solution on YOUR website!

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:

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: . This allows us to "move" an exponent from the argument "out in front":

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