Question

What is the base of the natural logarithm function f(x) = ln(x)? Explain how you know.

Answer 1

base = e

Explanation:

The general log function is defined as

`f(x)=\log_a x` .... (1)

where, a is the base of the log function.

The natural logarithm function is

`f(x)=\ln x`

It can be rewritten as

`f(x)=\log_e x` .... (2)

where, e is a constant or Euler's number is:

e ≈ 2.71828183

On comparing (1) and (2) we get

`a=e`

Therefore, the base of the natural logarithm function is e.