Chapter 4 - Exponential and Logarithmic Functions - Section 4.6 Logarithmic and Exponential Equations - 4.6 Assess Your Understanding - Page 338: 94

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

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).