# Natural Logarithm

How to solve the natral logarithm problems: definition, example, and its solution.

## Definition

The natural logarithm is a logarithm

with the base *e* (= 2.718... ).

Definition of *e* (mathematical constant)

It is written as [ln].

So log_{e} *c* = ln *c*.

## Example: Simplify ln 2*e*^{x + 1} (ln 2 = 0.69)

ln 2*e*^{x + 1} = ln 2 + ln *e*^{x + 1}

Logarithm of a product

ln *e*^{x + 1} = (*x* + 1) ln *e*

Logarithm of a power

ln 2 = 0.69

ln *e* = log_{e} *e*

So ln *e* = 1.

Logarithm of the base

(*x* + 1)⋅1 = *x* + 1

0.69 + 1 = 1.69

So (given) = *x* + 1.69.