Question

What is the natural log of zero?

Answer 1

Determine the value of the natural log of zero.

The definition of a logarithm is defined as:

$\begin{array}{rcl}{\log }_e\left(b\right)& =& x\\ & \Rightarrow & b=e^x\end{array}$

The natural log function of $0$ is represented by ${\log }_e\left(0\right)$ and the natural log of $0$ is represented by $\ln \left(0\right)$.

Replace $b$ with $0$ in the definition of logarithm.

$\begin{array}{rcl}{\log }_e\left(0\right)& =& x\\ & \Rightarrow & \ln \left(0\right)=x\\ & \Rightarrow & e^x=0\end{array}$

When $x$ equals to any value, there is no number that satisfy the equation $\begin{array}{rcl}{e}^x& =& 0\end{array}$.

Thus, the value of ${\log }_e\left(0\right)$ is undefined.

Hence, the value of ${\log }_e\left(0\right)$ is undefined.