The natural logarithm is a logarithm with which base?

• A. A logarithm with base 2
• B. A logarithm with base 10
• C. A logarithm with base e
• D. A natural number value

Answer: (C)

The natural logarithm uses base e, where e is about 2.71828. In calculus, ln x is the inverse of the exponential e^x, which makes its derivative particularly simple: d/dx (ln x) = 1/x, and e^(ln x) = x. This natural pairing is why we call it the natural logarithm. Other bases exist (base 2 for a binary logarithm, base 10 for the common logarithm), but they are different logarithms. So the natural logarithm is the logarithm with base e.