Natural Logarithm

Natural Logarithm

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

Definition

The natural logarithm is a logarithm with base e. log_e c = ln c.

The natural logarithm is a logarithm
with the base e (= 2.718... ).

Definition of e (mathematical constant)

It is written as [ln].
So loge c = ln c.

Example: Simplify ln 2ex + 1 (ln 2 = 0.69)

Simplify the given expression. ln 2e^(x + 1) (Assume ln 2 = 0.69.)

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

Logarithm of a product

ln ex + 1 = (x + 1) ln e

Logarithm of a power

ln 2 = 0.69

ln e = loge e

So ln e = 1.

Logarithm of the base

(x + 1)⋅1 = x + 1

0.69 + 1 = 1.69

So (given) = x + 1.69.