The best way to create that type of axes is to use the semilogy function. Alternatively, you can set the ‘YScale’ property on the axes: set(gca, 'YScale', 'log') ***Update from Mathworks Support Team - September 2023*** As of R2023b, you can also use the 'yscale ' function.

Maybe something like this? % data: X = 2*logspace(1, 3, 100); Y = rand(100,1); % labels to keep: labels = [20 30 50 70 100 200 300 500 1000 2000]; % prepare axes, plot: ax = axes('XScale', 'log', 'NextPlot', 'add'); plot(ax, X, Y, '.') ax.XLim = [20 2000]; ax.XAxis.TickDirection = 'out'; % steal the tick locations from the minor ticks, then turn the minor ticks off: drawnow ax.XTick = ax.XAxis.MinorTickValues; ax.XMinorTick = 'off'; % remove labels we don't want to keep: ax.XTickLabel(~ismember(ax.XTick, labels)) = {''};

scatter(1:10,1:10) set(gca,'xscale','log')

Alternatively, set(gca,'XScale','log') if you have your plot already.

The scale is still 'log'. However, because MATLAB automatically scales the axes to fit the data, the plot appears to be using cartesian scaling because your Y data ranges from 100 to 107. See this example. You could adjust the YLmin so that it is easier to see the logarithmic scale. As an aside, I suggest using logspace to create w. The vector will be much smaller, making it much easier to plot the results (I was getting errors running your code on my laptop). c_lead = 0.4018e-12; l_lead = 43.333e-9; wc = 2.488e+10; R = 100; w = logspace(4,9,10000); x = ((w./wc).^2)./((w.*c_lead).*(1+((w./wc).^2))); Zab = R./(1+((w./wc).^2)) + (w.*l_lead - x)*1i; loglog(w, (abs(Zab))); title('R = 100ohm'); xlabel('Frequency (in Hz)','FontSize',12,'FontWeight','bold','Color','r'); ylabel('Impedance (in ohm)','FontSize',12,'FontWeight','bold','Color','r'); grid on; Compare that to this plot figure loglog(w, (abs(Zab))); title('R = 100ohm'); xlabel('Frequency (in Hz)','FontSize',12,'FontWeight','bold','Color','r'); ylabel('Impedance (in ohm)','FontSize',12,'FontWeight','bold','Color','r'); grid on; ylim([1e2 1e4])