figure 
hold on
alpha = 0.3;

x = 0.3:0.01:2;
y = log(x);

h = plot(x, y, 'k');
set(h,'linewidth',3); % <- Set linewidth here

L = 1;
% Tangent line
a = 1.1;
x1 = (a-L/2):0.01:(a+L/2);
b1 = log(a);
y1 = (1/a)*(x1-a) + b1;
h = plot(x1, y1, 'g');
set(h,'linewidth',2); % <- Set linewidth here

x = log(0.3):0.01:log(2);
y = exp(x);

h = plot(x, y, 'k');
set(h,'linewidth',3); % <- Set linewidth here

L = 1;
% Tangent line
a = log(1.1);
x1 = (a-L/2):0.01:(a+L/2);
b1 = exp(a);
y1 = (exp(a))*(x1-a) + b1;
h = plot(x1, y1, 'g');
set(h,'linewidth',2); % <- Set linewidth here

x = -1:0.01:2;
h = plot(x, x, '--b');
set(h,'linewidth',2); % <- Set linewidth here


axis equal
axis off
% MATLAB does not have built-in SVG support. Use the following package to
% convert FIG files to SVG
plot2svg