I am having difficulties understanding how to solve the following problems:

1) Express as a single logarithm and, if possible, simplify:

$\displaystyle \frac{3}{2}ln4x^6 - \frac{4}{5}ln2y^{10}$

The book shows the answer as: $\displaystyle ln\frac{2^{11/5}x^9}{y^8}$

I understand how the $\displaystyle x^6$ turns into $\displaystyle x^9$, but how does the $\displaystyle 4$ in $\displaystyle \frac{3}{2}ln4x^6$ turn into $\displaystyle 2^{11/5}$?

2) Express as a single logarithm:

$\displaystyle 7lnx + 3(lny^2 - lnz^3)$

Since #1 is similar to #2, I am unsure on how to correctly solve this problem.

3) Find the inverse function of:

$\displaystyle f(x) = \frac{3x}{x-3}$

When I do the math, it shows that the inverse function is exactly the same as the original function? How is that possible?

I would appreciate it greatly if you could answer the questions above step-by-step.

Thanks