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Easy quick log question!

  1. Jun 24, 2004 #1
    Does
    [tex](\log_{x}a - \log_{x}b - \log_{x}c) = \log_{x}(\frac{a}{b/c})[/tex]?
     
  2. jcsd
  3. Jun 24, 2004 #2

    chroot

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    No, it equals

    [tex]\log_{x}(\frac{a}{b \cdot c})[/tex]

    Perhaps you just made a mistake. [itex]a/b[/itex] divided by [itex]c[/itex] is [itex]a/(b \cdot c)[/itex].

    - Warren
     
  4. Jun 24, 2004 #3

    chroot

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    An easy way to remember this is to remind yourself of the log rule:

    [tex]\log_x a^{-1} = - \log_x a[/tex]

    Whenever you see a minus sign in front of a log, mentally convert it to a plus sign and apply a -1 exponent to the argument. Then, when you add the logs, you multiply the arguments:

    [tex]a \cdot b^{-1} \cdot c^{-1} = \frac{a}{b \cdot c}[/tex]

    - Warren
     
  5. Jun 26, 2004 #4

    HallsofIvy

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    [tex] \log_{x}(\frac{a}{b/c})[/tex]
    would be
    [tex](\log_{x}a - (\log_{x}b - \log_{x}c)) [/tex]

    see the difference?
     
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