# Natural Logarithm

How to use the natural logarithm to simplify the given logarithm: definition, 1 example, and its solution.

## Definition

A natural logarithm (natural log)

is a logarithm

whose base is the natural constant e.

[log_{e}] is written as [ln].

## Exampleln 2e^{x + 1}

Solution

Solution (Detail)

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

Logarithm of a Product

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

Logarithm of a Power

It says

assume ln 2 = 0.69.

So ln 2 = 0.69.

Write +(x + 1).

ln e

= log_{e} e

= 1

Logarithm of Itself

So

ln 2 + (x + 1) ln e

= 0.69 + (x + 1)⋅1.

+(x + 1)⋅1 = +x + 1

0.69 + x + 1 = x + 1.69

So

x + 1.69

is the answer.