# Chapter 6 - Inverse Functions - 6.3* The Natural Exponential Function - 6.3* Exercises - Page 452: 9

$x=ln\frac{1}{\sqrt (e-1)}$

#### Work Step by Step

Given: $e-e^{-2x}=1$ $e-1=e^{-2x}$ $(-2x)lne=ln(e-1)$ This implies $x=ln\frac{1}{\sqrt (e-1)}$

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