# Chapter 4 - Section 4.4 - Trigonometric Functions of Any Angle - Exercise Set - Page 576: 116

The solution set is $\left\{ \frac{\ln 4}{3} \right\}$ which equals to $0.46$.

#### Work Step by Step

Let us consider the following equation. \begin{align} & 9{{e}^{3x}}-4=32 \\ & 9{{e}^{3x}}=32+4 \\ & 9{{e}^{3x}}=36 \\ & {{e}^{3x}}=\frac{36}{9} \end{align} Solving further, ${{e}^{3x}}=4$ Take the natural logarithm on both sides. \begin{align} & 3x=\ln 4 \\ & 3x=1.386 \\ & x=\frac{1.386}{3} \\ & =0.46 \end{align}

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