Chapter 6 - Logarithmic Functions - 6.5 Solving Exponential Equations - 6.5 Exercises - Page 528: 64

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

$g(x) = 3.4(10)^{x}$ Let $g(x) = y$ $y = 3.4(10)^{x}$ Swap the variables $x$ and $y$ and then solve for $y$ to find the inverse: $x = 3.4(10)^{y}$ $\frac{x}{3.4} = (10)^{y}$ $y = \log_{10} (\frac{x}{3.4})$ $y = \log (\frac{x}{3.4})$ $g^{-1}(x) = \log (\frac{x}{3.4}).$