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Math Help - Simplify logarithmic expression?

  1. #1
    Junior Member
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    Simplify logarithmic expression?

    Simplify this logarithmic expression: log10(9/300)

    My work:
    log 10(9/300) = log10 9 - log10 300 = 0 - log10 9 (150 x 2) = ?

    So am I doing this right? What is the next step?
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  2. #2
    Super Member

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    Hello, tsmith!

    Simplify: . \log_{10}\left(\frac{9}{300}\right)

    \log_{10}\left(\frac{9}{300}\right) \;=\;\log_{10}\left(\frac{3}{100}\right)


    . . . . . . . . = \;\log_{10}(3) - \log_{10}(100)


    . . . . . . . . = \;\log_{10}(3) - \log_{10}(10^2)<br />


    . . . . . . . . -\; \log_{10}(3) - 2\cdot\underbrace{\log_{10}(10)}_{\text{This is 1}}


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

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  3. #3
    Junior Member
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    Thank you so much! I understand it completely now.
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