Chapter 11.6, Problem 39E

To determine

The value of given equation by using natural logarithms.

Answer to Problem 39E

The value of the given equation is about $1.3155$ .

Explanation of Solution

Given:

  $3^x=3\sqrt{2}$

Calculation:

From the given equation,

  $\begin{array}{l}{3}^x=3\sqrt{2}\\ \ln 3^x=\ln 4.2426\\ x\ln 3=\ln 4.2426\\ x\ln 3=1.4451\\ x=\frac{1.4451}{\ln 3}\\ x=\frac{1.4451}{1.0986}\\ x\approx 1.3155\end{array}$

The value of the given equation is about $1.3155$ .