A couple lines are necessary to rearrange your equation to give log10(N) as a funciton of log10(S). Not surprisingly, the result is a straight line:
m=-3;
k=5.00034535E+11;
S=0.5:0.5:1000;
log10N = log10(k) - m*log10(S);
figure(1)
plot(log10(S),log10N)
grid
xlabel('log_{10}(S)')
ylabel('log_{10}(N)')
