Answer
$h^{-1}(x) = \frac{\ln (\frac{x}{-2.4})}{\ln 4.7}$
Work Step by Step
$h(x) = -2.4(4.7)^{x}$
Let $h(x) = y$
$y = -2.4(4.7)^{x}$
Swap the variables $x$ and $y$ and then solve for $y$ to find the inverse:
$x = -2.4(4.7)^{y}$
$(4.7)^{y} = -\frac{x}{2.4}$
$y = \ln_{4.7} (\frac{x}{-2.4})$
$y = \frac{\ln (\frac{x}{-2.4})}{\ln 4.7}$
$h^{-1}(x) = \frac{\ln (\frac{x}{-2.4})}{\ln 4.7}.$
