Logarithmic growth

Any logarithm base can be used, since one can be converted to another by multiplying by a fixed constant.

[3] In more advanced mathematics, the partial sums of the harmonic series grow logarithmically.

[4] In the design of computer algorithms, logarithmic growth, and related variants, such as log-linear, or linearithmic, growth are very desirable indications of efficiency, and occur in the time complexity analysis of algorithms such as binary search.

[1] Logarithmic growth can lead to apparent paradoxes, as in the martingale roulette system, where the potential winnings before bankruptcy grow as the logarithm of the gambler's bankroll.

During this bacterial growth phase, the number of new cells appearing is proportional to the population.