Given the function f(x)=3^x, find the value of f^-1(27)

This is asking you to solve the equation ...

... 27 = 3^x

You can use logarithms to find

... log(27) = x·log(3)

... log(27)/log(3) = x = 1.43136376.../0.47712125...

... x = 3

Or, you can use your knowledge of small cubes and match exponents.

... 3^3 = 3^x

... 3 = x

its 50 miles away from the starting point

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)