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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 aa can be written where bb indicates which base has been used. The expression is read as "log, base-bb, of aa" or "base-bb log aa".


For example, log4(16)=2,\log_{4}(16)=2, since 22 is the exponent used to raise the base 44 to get the number 16.16. Logarithms are undefined for negative values of a.a.

The relationship between base and exponent for logarithms and powers

The result of a logarithm depends on the base of the logarithm. Log base 4 indicates that the base is 44 while log base 9 has the base 9.9. If the base of the logarithm is changed the result of the logarithm becomes something else entirely.

The relationship between bases and exponents for different bases

The most common logarithms are base 10 logarithms, which are often written as lg\lg or log\log without a base for log10\log_{10}. The rules for logarithms apply to all bases.