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Math Help - Solving Log

  1. #1
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    Solving Log

    Given that log2=r, and log3=s, express the following in terms of r and s.
    log18 and log15

    I think I did the first one right, but I'm not sure
    =log(3x3x2)
    =log3+log3+log2
    =s+s+r
    =2s+r

    But I'm not sure how to do the second one.
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  2. #2
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    Lexington, MA (USA)
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    Re: Solving Log

    Helo, brian890!

    Given that: . \log2=r\,\text{ and }\,\log3=s,
    express the following in terms of r and s.

    (a)\;\log(18)

    I think I did the first one right, but I'm not sure

    \log(18) \:=\:\log(3\!\times\!3\!\times\!2) \:=\:\log3\!+\!\log3\!+\!\log2 \;=\;s\!+\!s\!+\!r \;=\;2s+r
    Right!

    (b)\;\log(15)

    I assume these logs are base-ten.

    We have: . \log_{10}(15) \:=\:\log_{10}\left(\frac{3\cdot10}{2}\right)

    . . . . . . . . . . . . . . . =\:\log_{10}(3) + \log_{10}(10) - \log_{10}(2)

    . . . . . . . . . . . . . . . =\; s + 1 - r

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