# Simplifying Log. Problem

• Mar 2nd 2010, 07:27 AM
Savior_Self
Simplifying Log. Problem
Hey guys. Alright, here's the problem:

(not sure how to do log base 3 in LaTex.. so log.3 = log base 3)

Expand as the sum of individual logarithms, each of whose argument is linear. Simplify your answer: $log.3(\frac{(x + 1)^3 \sqrt{y}}{\sqrt{y + 3}(x + 1)^2})$

I expanded it...

$log.3((x + 1)^3 y^\frac{1}{2}) - log.3((y + 3)^\frac{1}{2}(x + 1)^2)$

but I'm not sure how to go about simplifying it further.. Any help is greatly appreciated. Thanks!
• Mar 2nd 2010, 08:01 AM
Quacky
I'd start by cancelling the fraction.
$
Log[\frac{(x+1)^3\sqrt{y}}{\sqrt{y+3}(x+1)^2}]
$

$
=Log[\frac{(x+1)\sqrt{y}}{\sqrt{y+3}}]
$

$=Log[(x+1)y^{\frac{1}{2}}]-Log[(y+3)^\frac{1}{2}]$

$
=Log(x+1)+Log(y^\frac{1}{2})-Log[(y+3)^{\frac{1}{2}}]
$

This is, intentionally on my part, slightly unfinished. I have omitted the base 3 for clarity, but remember to keep it with all stages of working.

Someone will need to check my working, as I tend to make careless mistakes.
• Mar 2nd 2010, 08:26 AM
Savior_Self
Looks right to me. Thanks, Quacky!