Logarithmic growth

Logarithmic growth describes a quantity whose size or cost can be expressed as a logarithm of some input, in a relationship where the quantity equals a constant multiplied by the logarithm of the input. It is the inverse of exponential growth and increases very slowly, as seen in the number of digits needed to represent a number in a given base, which grows logarithmically in the size of that number, and in the partial sums of the harmonic series, which also grow logarithmically. In computer science, logarithmic growth appears in the time complexity of algorithms such as binary search. The term is also applied, somewhat confusingly, to the exponential growth phase of a bacterial culture, a usage that arises because exponential growth curves appear as straight lines when plotted on a logarithmic scale.