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

Question 1099475: Expand as the sum of individual logarithms, each of whose argument is linear. Simplify your answer.

-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(13214) (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:
,br>
Of course, there was also the option to do the simplification before taking the logarithm....
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
If you are a registered user, you can edit your submissions.
RELATED QUESTIONS
Expand as the sum of individual logarithms, each of whose argument is linear. Simplify... (answered by Fombitz)
Expand as much as possible into individual logarithms: log2 {(sqrt(x)(x-5))/y^3}... (answered by jsmallt9)
Hi Use the Laws of Logarithms to expand the expression... (answered by jim_thompson5910)
write each expression as a sum or difference of logarithms: ln(x^2 sqrt 1-x) ln... (answered by lwsshak3)
Express as a sum or difference of logarithms: • log a sqrt(x^4/y^3... (answered by greenestamps)
Express ln [(x^4 sqrt(x+1) / (x + 2)3 ] as the sum and difference of logarithms (answered by stanbon)
How do I use the properties of logarithms to expand this expression as a sum, difference, (answered by ewatrrr)
Use rational exponents to write x^1/5*y^1/3*z^1/6 as a single radical expression. I... (answered by Fombitz,jim_thompson5910)
1)Evaluate the logarithms using the change of base formula. Round your result to three... (answered by stanbon)