The minimal model program works with pairs $(X,B)$ where $X$ is a variety and $B$ is a certain kind of divisor on it. I've seen these described as "logarithmic pairs". There are also "log resolutions", "log canonical singularities" and so on.

What do these things have to do with logarithms?

The minimal model program works with pairs $(X,B)$ where $X$ is a variety and $B$ is a certain kind of divisor on it. I've seen these described as "logarithmic pairs". There are also "log resolutions", "log canonical singularities" and so on.

Question: What do these things have to do with logarithms?