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The natural logarithm that is a logarithm with base e ≈ 2.718 i.e. log_e 2, log_e 3. It is so popular that has shorten notation i.e. log_e 2 = ln 2, log_e 3 = ln 3. Using natural logarithms and formula log_a b = log_c b / log_c a can calculate logarithm with any base i.e. log_37 = ln 7 / ln3 ≈ 1.95 / 1.1 ≈ 1.77. This way is useful if a calculator has only key with a natural logarithm.