Chapter 8.7, Problem 62HP

To determine

To explain: The natural log can be used to solve a natural base exponential function.

Answer to Problem 62HP

The value of exponential is $\text{1}.\text{6}0\text{94}$ .

Explanation of Solution

Consider any natural base $(e^{})$ exponential function that is independent variable will be as an exponent of $e^{}$ . For example,

  $e^x=5$

To solve this type of equation there are no such method which can explicitly give the value of $x$ .only trail and error method can be applies to obtain it but it is very difficult to find $x$ with higher degree of precision.

Here comes the beauty of natural logarithm which explicitly gives the value of $x$ and which can be easily obtain by calculator or corresponding logarithmic table such as for the chosen problem.

Taking logarithm of base $e$ of both side.

  $\begin{array}{c}In{e}^x=In5\\ x=In5\\ =\text{1}.\text{6}0\text{94} \end{array}$

Therefore, the value of exponential is $\text{1}.\text{6}0\text{94}$ .