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

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

The book shows the answer as:

I understand how the turns into , but how does the in turn into ?

2) Express as a single logarithm:

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

3) Find the inverse function of:

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