The base for natural logarithms is which number?

• A. 2
• B. 10
• C. e
• D. pi

Answer: (C)

Natural logarithms arise as the inverse of the exponential function with a special base chosen to make calculus neat. that base is e, about 2.718. The reason e is singled out is that the growth rate of e^x matches itself: d/dx e^x = e^x. This leads to a clean derivative for the natural log: d/dx ln x = 1/x. If you used a different base, like 10, the derivative would be 1/(x ln 10), which adds an extra constant and complicates calculations. So the base of natural logarithms is e, not 2, 10, or pi.