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Math Help - Simple Log Help!

  1. #1
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    Simple Log Help!

    If x = log2 and y = log3, express the following in terms of x and y:

    c) log15
    h) log0.27
    j) log0.6
    l) log1.8

    Thanks!

    PS. All bases are 10.
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  2. #2
    Super Member Matt Westwood's Avatar
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    As 15 = 30 / 2 you can express it as 10 * 3 / 2

    Log 10 = 1, and you have log 3 and log 2 so use the standard combination laws: log xy = log x + log y, log (x/y) = log x / log y.

    Others solved the same way - the tricksy bit here is the fact that you have powers of 10 in the mix.
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  3. #3
    MHF Contributor Unknown008's Avatar
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    Just remember your rules:

    \log\ a + \log\ b = \log\ ab

    \log\ a - \log\ b = \log\ \dfrac{a}{b}

    What can you come up with?
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  4. #4
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    Quote Originally Posted by eskimogenius View Post
    If x = log2 and y = log3, express the following in terms of x and y:

    c) log15


    15=\frac{3}{2}\cdot 10 , and now look below.


    h) log0.27


    0.27=(0.3)\cdot (0.9)\Longrightarrow since \log(a\cdot b)=\log a\cdot \log b , then...



    j) log0.6


    Just note that 0.6=2\cdot (0.3)\,,\,\,0.3=\frac{3}{10}\,\,and\,\,\log(a/b)=\log a-\log b


    l) log1.8


    1.8=3\cdot 0.6 ...

    Tonio



    Thanks!

    PS. All bases are 10.
    .
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  5. #5
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    Thanks for that. Should have thought about the questions more before I blogged them.

    Sorry.
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  6. #6
    Super Member Matt Westwood's Avatar
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    Quote Originally Posted by eskimogenius View Post
    Thanks for that. Should have thought about the questions more before I blogged them.

    Sorry.
    You're all right. No worries. Enjoy your time here.
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