Hello, Remriel!
I know the answer . . . . I'm always impressed by that!
We are given: .
Switch variables: .
m . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . . . . . . .
Take logs, base 2: .
. . . . . . . . . . . . .
Therefore: .
We can manipulate Prove It's answer to get your one using the log laws.
By the subtraction rule:
By the change of base rule: of which the RHS is the safe as the expression above.
Putting in the expression for y:
Thus the two answers are equivalent.
Also note that for the inverse - what does that tell you about the original function's range (admittedly you don't need to include this bit for your question)