Chapter 3.3, Problem 29E

Solution

To evaluate: the given logarithmic expression if it is defined using a calculator, and check your result by evaluating the corresponding exponential expression.

  $\ln 4.05\approx 1.399$

Given information:

The expression:

  $\ln 4.05$

Definition Used:

Natural logarithm- Base e :

The Natural logarithmic function ${\log }_{e}x=\ln x$ is the inverse of the exponential function $f\left(x\right)=e^x$ . Therefore,

  $y=\ln x$ if and only if $e^y=x$

Explanation:

First use a calculator to evaluate $\ln 4.05$ .

  

So,

  $\begin{array}{c}\ln 4.05=1.398716881\\ \approx 1.399\end{array}$

Now, evaluating the corresponding exponential expression.

By the above definition of natural logarithm:

  $y=\ln x$ if and only if $e^y=x$

Applying this to the given function:

  $\ln 4.05=1.398716881$ if and only if $e^{1.398716881}=4.05$

So, checking this using a calculator,