Chapter 4 - Exponential and Logarithmic Functions - Section 4.6 Logarithmic and Exponential Equations - 4.6 Assess Your Understanding - Page 338: 92

$ln(3\pm2\sqrt 2)\approx \pm1.763$

1. $\frac{e^x+e^{-x}}{2}=3 \Longrightarrow 2e^x(\frac{e^x+e^{-x}}{2})=6e^x \Longrightarrow e^{2x}-6e^x+1=0 \Longrightarrow e^x=\frac{6\pm\sqrt {36-4}}{2}=3\pm2\sqrt 2 \Longrightarrow x=ln(3\pm2\sqrt 2)\approx \pm1.763$ 2. Check, $x=ln(3\pm2\sqrt 2)$ fit(s).