The number e, 2.718281828..., was chosen as the "natural" base for logarithms and powers because it is the only number where the deriviative of e to the x is x...
d/dy ex = x
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The natural logarithm (ln) is used when you have log base e
The natural logarithm is calculated to base e, where e is Euler's constant. For any number, x loge(x) = log10(x)/log10(e)
The logarithm of 1.5 is approximately 0.1760912591... Your logarithm is base 10, and the natural logarithm of 1.5 (base e), is approximately 0.4054651081... Example base: 8 Approximately: 0.1949875002...
Zero, in logs to base 10, base e, or any base.
Assuming you mean 'logarithm to the base 'e' ( natural logarithm. On the calculator its symbol is 'ln'. Hence ;ln 2 = 0.69314718....