such that , the logarithm of a positive real number with respect to base is the exponent by which must be raised to yield . In other words, the logarithm of to base is the unique real number such that .

The logarithm is denoted "" (pronounced as "the logarithm of to base ", "the base-{{mvar}} logarithm of ", or most commonly "the log, base , of ").

An equivalent and more succinct definition is that the function is the inverse function to the function .

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