You original function was . The basic definition of "inverse functions" requires that and . not x. Similarly , not x.
A standard method of finding the inverse of a function given as y= f(x) is
1) Swap x and y (that's the key point).
2) Solve the equation for y.
3) If there is a unique solution for y as a function of x, that is the inverse.
Here, . Swapping x and y, . To solve for y, first, divide both sides by 3: . Now take 10 to the power of both sides: . Since , that is the inverse function.