Chapter 6 - Logarithmic Functions - 6.2 Logarithmic Functions - 6.2 Exercises - Page 504: 94

$g^{-1}(x) = \log_5 \frac{x}{6}$

$g(x) = 6(5^{x})$ Let $g(x) = y$ $y = 6(5^{x})$ Swap the $x$ and $y$ variable to find the inverse: $x = 6(5^{y})$ $\frac{x}{6} = 5^{y}$ $y = \log_5 \frac{x}{6}$ $g^{-1}(x) = \log_5 \frac{x}{6}$