SOLUTION: Expand as the sum of individual logarithms, each of whose argument is linear. Simplify your answer. {{{ (((x+1)^3) (sqrt(y)))/(sqrt(y+3)(x+1)^2) }}} -Accidentally submitted th

Algebra ->  College  -> Linear Algebra -> SOLUTION: Expand as the sum of individual logarithms, each of whose argument is linear. Simplify your answer. {{{ (((x+1)^3) (sqrt(y)))/(sqrt(y+3)(x+1)^2) }}} -Accidentally submitted th      Log On


   

Question 1099475: Expand as the sum of individual logarithms, each of whose argument is linear. Simplify your answer. +%28%28%28x%2B1%29%5E3%29+%28sqrt%28y%29%29%29%2F%28sqrt%28y%2B3%29%28x%2B1%29%5E2%29+

-Accidentally submitted this question before I was done writing it, so that's why there's a second question like this one.
Found 2 solutions by greenestamps, richwmiller:
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!

By the laws of exponents, and therefore by the laws of logarithms, when you take logarithms, all exponents come out in front as multipliers of the logarithms.

And roots are fractional powers; in this example, each square root is a one-half power.

And then of course you need to use the rules that say multiplying means adding logarithms and dividing means subtracting logarithms.

Put that all together and we get


There are two terms with log(x+1) which can be combined:
log%28%28x%2B1%29%29%2B%281%2F2%29log%28y%29-%281%2F2%29log%28%28y%2B3%29%29,br>
Of course, there was also the option to do the simplification before taking the logarithm....

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
If you are a registered user, you can edit your submissions.