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Plots of logarithm for bases 0.5, 2 and e. In mathematics, the logarithm is the inverse operation to exponentiation, just as division is the inverse of multiplication and vice versa. That means the logarithm of a number is the exponent to which another fixed number, the base, must be raised to produce that number. In simple cases the logarithm counts factors in multiplication.
On calculators it is usually log, but mathematicians usually mean natural logarithm (logarithm with base e â 2.71828) rather than common logarithm when they write log. To mitigate this ambiguity the ISO 80000 specification recommends that log 10 (x) should be written lg (x) and log e (x) should be ln (x).he logarithm keys (log for base-10 and ln for base-e) on a typical scientific calculator. The advent of hand-held calculators largely eliminated the use of common logarithms as an aid to computation. The numerical value for logarithm to the base 10 can be calculated with the following identity.