Log law -Change base

  • Thread starter dilan
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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
 

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  • #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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