# How do you find the domain and range of a natural log?

Feb 19, 2015

Hello,

The natural logarithm, also called neperian logarithm, is noted $\ln$.

The domain is D=]0,+\infty[ because $\setminus \ln \left(x\right)$ exists if and only if $x > 0$.

The range is I=RR = ]-oo,+oo[ because $\ln$ is strictly croissant and $\setminus {\lim}_{x \setminus \to - \infty} \ln \left(x\right) = 0$ and $\setminus {\lim}_{x \setminus \to + \infty} \ln \left(x\right) = + \infty$.

graph{ln(x) [-2.125, 17.875, -4.76, 5.24]}

The domain $D$ is the projection of the curve of $\ln$ on the x axe.

The range $I$ is the projection of the curve on y axe.