What I Understood:
In a logarithmic function, when one gives an input, it will output the exponenent of the given base. For example, if one input 8 into log base 2 the output will be 3.
To find out if the inverse of a function is possible, one may use the horizantol line test the same way one uses the vertical line test to determine of a graph is a function.
The inverse of a fucntion, wether it is a fucntion or not, is mirrored about the line y=x. This makes graphing the inverse of a graph much easier.
The inverse of in exponent is a logarithm.
Misunderstood:
how to solve a piece wise function with a log
how to apply transformtion of a log function