Difference between revisions of "Logarithm"
(fixed TeX; \log should be used for logs) |
m (log>\log) |
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These hold for all logarithms. | These hold for all logarithms. | ||
*<math>\log_a b^n=n\log_a b</math> | *<math>\log_a b^n=n\log_a b</math> | ||
| − | *<math>log_a b+ \log_a c=\log_a bc</math> | + | *<math>\log_a b+ \log_a c=\log_a bc</math> |
*<math>\log_a b-\log_a c=\log_a \frac{b}{c}</math> | *<math>\log_a b-\log_a c=\log_a \frac{b}{c}</math> | ||
*<math>(\log_a b)(\log_c d)= (\log_a d)(\log_c b)</math> | *<math>(\log_a b)(\log_c d)= (\log_a d)(\log_c b)</math> | ||
*<math>\frac{\log_a b}{\log_a c}=\log_c b</math> | *<math>\frac{\log_a b}{\log_a c}=\log_c b</math> | ||
*<math>\log_a^n b^n=\log_a b</math> | *<math>\log_a^n b^n=\log_a b</math> | ||
Revision as of 09:03, 22 June 2006
A logarithm is a shorthand way of expressing exponentional notation.
Introductory
The general form for a logarithm can be expressed as 
which means 
. We would read this as "The logarithm of y base x is z".
We have 
. To express this in Logarithmic notation, we would write it as 
.
When a logarithm has no base, it is assumed to be base 10.
Logarithmic Properties
These hold for all logarithms.
