# What should I assume when I see log?

1. Sep 30, 2013

### 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?

2. Sep 30, 2013

### phinds

I'm with you.

3. Sep 30, 2013

### Integral

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

4. Sep 30, 2013

### mathman

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).

5. Sep 30, 2013

### AlephZero

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

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).

6. Sep 30, 2013

### 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.

7. Oct 1, 2013

### arildno

In certain professional fields, such as in some cases in fluid mechanics, established tradition uses log_10 constants in a few, handy formulae (I was in much surprize and consternation when I met them! The author had at least the minimal decency to write, explicitly, log_10, rather than log).
Otherwise, log_10 is basically eliminated from the professional world.