Chapter 4 - Exponential and Logarithmic Functions - Section 4.6 Logarithmic and Exponential Equations - 4.6 Assess Your Understanding - Page 338: 93

$ln(2+\sqrt 5)\approx 1.444$

1. $\frac{e^x-e^{-x}}{2}=2 \Longrightarrow 2e^x(\frac{e^x-e^{-x}}{2})=4e^x \Longrightarrow e^{2x}-4e^x-1=0 \Longrightarrow e^x=\frac{4\pm\sqrt {16+4}}{2}=2\pm\sqrt 5 \Longrightarrow x=ln(2+\sqrt 5)\approx 1.444$ 2. Check, $x=ln(2+\sqrt 5)$ fit(s).