This line of code is supposed to generate exponential service times, but I am not able to get the logic behind it

This line of code is supposed to generate exponential service times, but I am not able to get the logic behind it.

% Exponential service time with rate 1 mean = 1; dt = -mean * log(1 - rand());

This is the source link, but MATLAb is needed to open the example.

I was also thinking if exprnd(1) will give the same result of generating numbers from the exponential distribution that has mean = 1?