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# Logarithm

A logarithm is a number that indicates an exponent used to raise a logarithm's base in order to get back an indicated number. The logarithm of a positive number $a$ can be written where $b$ indicates which base has been used. The expression is read as "log, base-$b$, of $a$" or "base-$b$ log $a$".

$\log_{b}(a)$

For example, $\log_{4}(16)=2,$ since $2$ is the exponent used to raise the base $4$ to get the number $16.$ Logarithms are undefined for negative values of $a.$

The result of a logarithm depends on the base of the logarithm. Log base 4 indicates that the base is $4$ while log base 9 has the base $9.$ If the base of the logarithm is changed the result of the logarithm becomes something else entirely.

The most common logarithms are base 10 logarithms, which are often written as $\lg$ or $\log$ without a base for $\log_{10}$. The rules for logarithms apply to all bases.