#### Answer

$f^{-1}(x) = \log_6 (\frac{x}{3.5} )$

#### Work Step by Step

$f(x) = 3.5(6)^{x}$
Let $f(x) = y$
$y = 3.5(6)^{x}$
Swap the variables $x$ and $y$ and then solve for $y$ to find the inverse:
$x = 3.5(6)^{y}$
$\frac{x}{3.5} = (6)^{y}$
$y = \log_6 (\frac{x}{3.5} )$
$f^{-1}(x) = \log_6 (\frac{x}{3.5} )$