Inverse of an exponential function

Question

I am having difficulties forming the inverse of this $f(x) = 3 \cdot2^{3x+1} \cdot 5^{3x-1}$.

What I have done so far:

$3 \cdot 2^{3y} \cdot 2^1 \cdot 5^{3y}\cdot5^{-1} \Leftrightarrow 3\cdot 2\cdot \frac{1}{5}\cdot (5\cdot 2)^{3y} \Leftrightarrow \frac{6}{5}\cdot 10^{3y} \Leftrightarrow \ln \frac{6}{5}\cdot \ln10\cdot 3y$

Answer 1

You just need to finish it. $$x = \frac65*10^{3y}$$ $$10^{3y} = \frac56*x$$ $$3y*\ln10 = \ln(\frac56*x)$$ $$y = \frac {\ln(\frac56*x)} { 3*\ln10}$$

Answer 2

$x = \frac{\log \left(\frac{y}{6}\right)+\log (5)}{3 (\log (2)+\log (5))}$.