Natural Logarithm

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

Definition

Definition

A natural logarithm (natural log)
is a logarithm
whose base is the natural constant e.

[loge] is written as [ln].

Example

Example

Solution

ln 2ex + 1 = ln 2 + ln ex + 1

Logarithm of a Product

+ln ex + 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
= loge 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.