Chapter 4.5, Problem 9E

To determine

To calculate: The solution of the exponential , rounded to four decimal places , $3e^x=10$

Answer to Problem 9E

The four decimal places rounded value of exponential expression,$x=0.5228$

Explanation of Solution

Given information:

The given expression is as, $3e^x=10$

Formula used:

For the exponential expression take log on both sides.

These are the steps to do this ,

  $\log a^x=x\log a,\log e^x=x\log e$

Step 1 take log both side.

Step 2. Then to find the value of x one side take all the values of x and another side all the values of log and constants .

Step 3. Then with the help of log table put the value of log .

Step 4. Take the four decimal value of x from there .

Calculation :

Consider the expression, $3e^x=10$

Take logarithms both sides.

  $\begin{array}{c}3e^x=10\\ e^x=\frac{10}{3}\\ \log e^x=\log \frac{10}{3}\end{array}$

Apply the identity: $\log a^x=x\log a$

  $\begin{array}{c}\log e^x=\log \frac{10}{3}\\ x\log e=\log \frac{10}{3}\\ x=\log \frac{10}{3}\end{array}$

Apply the value of $\log \frac{10}{3}$ :

Rewrite the expression: $\begin{array}{l}x=\log \frac{10}{3}\\ x=0.5228\end{array}$

The above expression can’t be simplified further.

Thus the simplified form of the expression is $x=0.5228$ .