Definition of Natural Logarithm

Reference > Algebra: Natural Logarithms

Description

The Definition of Natural Logarithm Rule states that:

ey=x{e}^{y}=x if and only if lnx=y\ln{x}=y
Examples
e4x=3{e}^{4x}=3
1
Use Definition of Natural Logarithm: ey=x{e}^{y}=x if and only if lnx=y\ln{x}=y.
4x=ln34x=\ln{3}

2
Divide both sides by 44.
x=ln34x=\frac{\ln{3}}{4}

Done

Decimal Form: 0.274653