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Math Help - Simplification of Logs

  1. #1
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    Exclamation Simplification of Logs

    logbase10(1/10) − logbase10(10/27) − logbase10 1000

    I know all the rules for simplifying logs, however I cant seem to get this one right!

    If any one could show me some working out towards the end of the simplification that would be great.

    Thanks in advance for any help.

    Mike
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by mikewhant View Post
    logbase10(1/10) − logbase10(10/27) − logbase10 1000

    I know all the rules for simplifying logs, however I cant seem to get this one right!

    If any one could show me some working out towards the end of the simplification that would be great.

    Thanks in advance for any help.

    Mike
    log_{10}(0.1) = -1

    <br />
log_{10}\left(\frac{10}{27}\right) = log_{10}(10) - 3log_{10}(3) (because 27 = 3^3)

    log_{10}(1000) = log_{10}(10^3) = 3

    So your sum reduces to -1-(1-3log_{10}(3))-3
    Last edited by e^(i*pi); December 9th 2009 at 11:02 AM. Reason: indeed it should be -3
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  3. #3
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    Thats great, just one further question, why is it + 3 on the end?

    I can see now that log 1000 = 3, however in the original expression, it was
    - log 1000, so should'nt it bee -3?

    Thaanks again

    Mike
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  4. #4
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by mikewhant View Post
    Thats great, just one further question, why is it + 3 on the end?

    I can see now that log 1000 = 3, however in the original expression, it was
    - log 1000, so should'nt it bee -3?

    Thaanks again

    Mike
    Yes it should, that was an oversight on my part

    Thanks for pointing it out
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  5. #5
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    Ah right ok, lol, funny because what was stumping me in the first place was the text book i have the question from gives the same answer you gave, + 3!

    Anyway, thanks for that, all cleared up now!

    Take care

    Mike
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