Chapter 6 - Logarithmic Functions - 6.5 Solving Exponential Equations - 6.5 Exercises - Page 528: 67

$g^{-1}(x) = \ln_ (\frac{x}{-3.4})$

$g(x) = -3.4e^{x}$ Let $g(x) = y$ $y = -3.4e^{x}$ Swap the variables $x$ and $y$ and then solve for $y$ to find the inverse: $x = -3.4e^{y}$ $(e)^{y} = -\frac{x}{3.4}$ $y = \ln (\frac{x}{-3.4})$ $y = \ln_ (\frac{x}{-3.4})$ $g^{-1}(x) = \ln_ (\frac{x}{-3.4}).$