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Math Help - Simplifying Log. Problem

  1. #1
    Junior Member
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    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!
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  2. #2
    Super Member Quacky's Avatar
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    Windsor, South-East England
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    I'd start by cancelling the fraction.
     <br />
Log[\frac{(x+1)^3\sqrt{y}}{\sqrt{y+3}(x+1)^2}]<br />

     <br />
=Log[\frac{(x+1)\sqrt{y}}{\sqrt{y+3}}]<br />

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

     <br />
=Log(x+1)+Log(y^\frac{1}{2})-Log[(y+3)^{\frac{1}{2}}]<br />

    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.
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  3. #3
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    Looks right to me. Thanks, Quacky!
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