# What should I assume when I see log?

Permanence
Today in a lecture in one of my engineering courses the professor said that mathematicians assume that when log is written the base is e. I had always learned to assume base 10, and simply write ln when I wanted the base as e.

Is my professor correct or is that a bad habit to adapt?

Gold Member
2021 Award
Today in a lecture in one of my engineering courses the professor said that mathematicians assume that when log is written the base is e. I had always learned to assume base 10, and simply write ln when I wanted the base as e.

I'm with you.

Staff Emeritus
Gold Member
In math and physics log10 is rarely used, assume base e. I also use ln for base e.

Context is the main determining factor. When doing analysis, assume e. When doing calculation, assume 10. Often to distinguish, base e is denoted by ln(x) rather than log(x).

Homework Helper
I had always learned to assume base 10, and simply write ln when I wanted the base as e.

That's a perfectly reasonable "rule", but don't expect everybody else to use it!

When doing calculation, assume 10

Well, calculator buttons are often labeled log and ln, but computer programming languages tend to use log() for base e and log10() for ... um .... some other base, maybe 42?

Just remember that one way to have a quiet life is use the same notation as your prof.

And number theorists think ##\log_k x## means ##\ln \ln \dots\ \ln x##. (i.e take the natural log k times).

eigenperson
In addition to mathematicians, who 99% of the time mean the natural log when they say "log", there are also computer scientists, who usually mean the log base 2.

In most cases, it's either clear from context or doesn't matter.