One exponential function is so important in mathematics that it is distinguished by calling it the exponential function. This exponential function is written as ${\ⅇ}^{x}$ or, particularly when the expression in the exponent is complicated, $\mathrm{exp}\left(x\right)$. The inverse of this function is just as important in mathematics.
The Natural Logarithm Function

The natural logarithm function is the inverse of the exponential function, ${\ⅇ}^{x}$, where $\ⅇequals;2.718281828..period;$ . This function is so important in mathematics, science, and engineering that it is given the name "ln": $\mathrm{ln}\left(x\right)\={\mathrm{log}}_{\ⅇ}\left(x\right)$. Reading out loud, it is pronounced "lawn of x" or often just "lawn x".



The graph of the natural logarithm function can be obtained from that of the exponential function by reflection across the line $y\=x$: