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Log law -Change base

  1. Jan 25, 2006 #1
    Hi,
    I am just a little confused with this log law of change base. Is there any one who can give me a clear description with an example?:smile:
    Thanks
     
  2. jcsd
  3. Jan 25, 2006 #2

    arildno

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    Let a,b>0, and distinct from 1 be the respective bases, and let c be an arbitrary positive number.

    Then, you evidently have:
    [tex]c=a^{log_{a}(c)}=b^{log_{b}(c)[/tex]
    Taking the logarithm with respect to a on both sides, you get:
    [tex]\log_{a}(c)=\log_{b}(c)\log_{a}(b)[/tex]
    that is:
    [tex]log_{b}(c)=\frac{log_{a}(c)}{log_{a}(b)}[/tex]
    Was that what you're after?
     
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