Definition of Natural Logarithm

Reference > Algebra: Natural Logarithms

Description

The Definition of Natural Logarithm Rule states that:

\({e}^{y}=x\) if and only if \(\ln{x}=y\)
Examples
\[{e}^{4x}=3\]
1
Use Definition of Natural Logarithm: \({e}^{y}=x\) if and only if \(\ln{x}=y\)
\[4x=\ln{3}\]

2
Divide both sides by \(4\)
\[x=\frac{\ln{3}}{4}\]

Done

Decimal Form: 0.274653