Chapter 6 - Logarithmic Functions - 6.2 Logarithmic Functions - 6.2 Exercises - Page 504: 93

$f^{-1}(x) = \log_4 \frac{x}{3}$

$f(x) = 3(4^{x})$ Let $f(x) = y$ $y = 3(4^{x})$ Swap the $x$ and $y$ variable to find the inverse: $x = 3(4^{y})$ $\frac{x}{3} = 4^{y}$ $y = \log_4 \frac{x}{3}$ $f^{-1}(x) = \log_4 \frac{x}{3}$