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This graph illustrates data plotted with a logarithmic x-axis, a logarithmic y-axis, and both logarithmic axes:



These graphs were obtained with the following commands.  Notice that when the limits of a logarithm graph is set, it MUST be set using the logarithm of that vector.  The points must also be called this way.  The ticksize command is responsible for the logarithmic spacing of the tickmarks.

           #both x and y log axis.
            clear
            set x=.001, 10, .001
            set y=10**x
            set lgx=lg(x)
            set lgy=lg(y)
            limits lgx lgy
            ticksize -1 0 -1 0
            box
            points lgx lgy
            ylabel log y axis
            xlabel log x axis
           
            expand .8
            #log x axis
            location 8000 20000 20000 30000
            ticksize -1 0 0 0
            limits lgx y
            box
            points lgx y
            xlabel log x axis
            ylabel y axis
           
            #log y axis
            location 8000 20000 8000 18000
            ticksize 0 0 -1 0
            limits x lgy
            box
            points x lgy
            xlabel x axis
            ylabel log y axis
           
            #resets values
            location  3500 31000 3500 31000
            ticksize 0 0 0 0
            expand 1.001
            delete lgx
            delete lgy
            delete x
            delete y