Semilog plot with background image

I've modelled lines from image files and now I want to check that what I've done is correct. I want to plot the equations I came up with on top of the image files. So far, I can create two different figures, but I cannot plot both on top of one another (preferably with the image file slightly transparent). I've see a solution for non-log plots, but cannot seem to find anything that would work in my case. See below the code, as well as 'sample.png'.

clear
clc
close all

%%Create X-Axis
x = linspace(0,100,1001);

%%Low Variables
al = 10.95138337;
bl = 7.440851134;
cl = 1.51185755;
dl = -0.162527357;

yl = al + bl*log(x) + cl*log(x).^2 + dl*log(x).^3;

semilogx(x,yl,'g')
hold on
grid on

%%Medium Variables
am = 20.6143819;
bm = 9.539354014;
cm = 1.206316519;
dm = -0.129084187;

ym = am + bm*log(x) + cm*log(x).^2 + dm*log(x).^3;

semilogx(x,ym,'y')

%%High Variables
ah = 30.29206721;
bh = 12.42540544;
ch = 1.390071294;
dh = -0.26660217;

yh = ah + bh*log(x) + ch*log(x).^2 + dh*log(x).^3;

semilogx(x,yh,'r')

%%Plot the image
 im = imread('sample.png');

   figure
   %define plot extent so that image can be aligned with plot
   xrng = [0 100];
   yrng = [0 100];
   imagesc(xrng,yrng,im);
   ax1 = gca;

   %get rid of pixel ticklabels
   set(ax1,'YTickLabel', [], 'XTickLabel', [])

   %color=none to make the image visible
   ax2 = axes('Position',get(ax1,'Position'),'Color','none','XScale', 'log');
   ylim(yrng)
   xlim(xrng)

[Star Strider]

See How to overlay a log-plot on top of an image for follow-up.