# Definition of Natural Logarithm

## Reference > Algebra: Natural Logarithms

 DescriptionThe 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}$DoneDecimal Form: 0.274653x=ln(3)/4