I am assuming that you want to find the inverse of the given logarithmic function and then draw the graph of the inverse function. If this is true, given below are the steps:
f(x) = y = 1/2 log (2x) so the inverse function is x= 1/2 log (2y) because x is replaced with y.
For graphing this inverse function, select few values of y for instance ( 1, 3 ,5 , 15) and find corresponding values of x by substituting these y values in the inverse function. This way you now have a set of ordered x,y pairs. (See below) . Plot these points and you have the graph of the inverse function.