Question 760115
The switching to the inverse function is because we want to be able to reverse a process.  Just as we want to know how to open a door and walk through it, we also want to open the door and come back the other way.  Just as we want to insert our foot into a shoe and tie the lace, we later want to untie the shoe and pull our foot out of it.


You have a logarithmic function f(x), and you put in some value for x and obtain some value of f(x) according to the defined formula.  Later, you might want to use the function that if you give the function f(x), this other function would give you back x.  


You are trying to find g(x) so that {{{f(g(x))=x}}} and that {{{f(x)=ln(x-3)}}}.

You can start this way:
g(x)=?
You want g(x) to be the inverse of {{{f(x)=ln(x-3)}}}.  You must have {{{g(f(x))=f(g(x))=x.}}}


{{{f(g(x))=ln((g(x))-3)=x}}}
That says, the natural log of some expression is equal to x.

Converting into exponential form,
{{{e^(x)=g(x)-3}}}
{{{g(x)-3=e^x}}}
{{{highlight(g(x)=3+e^x)}}}