Chapter 13.1, Problem 57E

To determine

To calculate: The value of x in the expression $x=e^{0.346}$ .

Answer to Problem 57E

The value of x in the expression $x=e^{0.346}$ is $1.4$ .

Explanation of Solution

Given information:

The expression $x=e^{0.346}$ .

Formula used:

The logarithmic function and exponential function cancel out each other that is $\log e=1$ .

The property of logarithmic function is $\log a^x=x\log a$ where $a>0$ .

Calculation:

Consider the expression $x=e^{0.346}$ .

Take logarithm on both the sides,

  $\log \left(x\right)=\log \left(e^{0.346}\right)$

Apply the property of logarithmic function that is $\log a^x=x\log a$ where $a>0$ .

  $\begin{array}{c}\log \left(x\right)=\log \left(e^{0.346}\right)\\ \log x=0.346\log e\\ \log x=0.346\end{array}$

Take antilog on both the sides and use a scientific calculator to simplify the above expression,

  $\begin{array}{c}\log \left(x\right)=\log \left(e^{0.346}\right)\\ \log x=0.346\log e\\ \log x=0.346\\ x\approx 1.4\end{array}$

Thus, the value of x in the expression $x=e^{0.346}$ is $1.4$ .