# Log(x) do you assume base 10 or base e?

1. Jul 28, 2014

### Matterwave

So, out of curiosity, when you guys see log(x) do you assume base 10 or base e?

Because I just wasted 2 hours of my life wondering how I got a problem wrong due to the fact that I assumed base e and the problem assumes base 10...

2. Jul 28, 2014

### WWGD

In my experience the base e usually goes with ln , and other bases go with log.

3. Jul 28, 2014

### Matterwave

Right, but if you just saw "log(x)" with no subscripts? I think in high school I would have defaulted to base 10 but now I default to base e.

I think google defaults to base 10 while Wolfram defaults to base e. FORTRAN defaults to base e, I'm not sure about other programming languages.

4. Jul 28, 2014

### olivermsun

I'd consider the context/audience.

Mathematicians, usually log is base e. Engineers and chemists, often base 10.

5. Jul 28, 2014

### symbolipoint

What was the problem you were working? Choose the base that makes sense for the situation or problem.

6. Jul 29, 2014

### Matterwave

It was a semi-long problem about numerically modeling the metalicity content of a galaxy. The log appeared in just one part of the problem. Astronomers are particularly icky when it comes to conventions. The part of the problem asked me to compute the fractional metalicity in terms of a log function:

$$[Fe/H](t)=12-\log\left(\frac{g_{Fe}(t)/55.845}{g_H(t)/1.008}\right) - 7.52$$

As an aside, notice that the astronomer put a 12 in front and a -7.52 at the end without combining it into a 4.48 because of convention... because the 12 and the -7.52 adjustments are made for 2 different reasons (which I do not know).

I suppose if I had thought about it enough, I might have figured out he meant log base 10, but I assumed log base e without thinking and proceeded to the next step. It took me roughly 2 hours to figure out that's where I went wrong.

Last edited: Jul 29, 2014
7. Jul 29, 2014

### NathanaelNolk

It greatly depends on the context. ln(x) should be used instead of log(x) when in base e. But I know that a lot of mathemathicians write log(x) when they should write ln(x).
log(x) without subscript usually means log base 10 (widely used in chemistry for instance).
When I have to do a computation with a log simply written as log(x) an I assume it's in base 10, but I always check the context.

8. Jul 29, 2014

### olivermsun

Why "should be"? One could just as easily say people should write log10 if that's what they mean.

9. Jul 29, 2014

### disregardthat

I always think of the base as e, and I think most mathematicians are. Logarithms in any other base can be cleanly expressed in terms of log with base e as a quotient: log_a(x) = log_e(x)/log_e(a), and as a mathematical function log(x) with base e have the neatest behavior (just like e^x).

10. Jul 29, 2014

### Matterwave

I meant with this thread to just ask about first instincts haha. I know one should look at the context, but this problem arose because I had the instinct to treat the log as base e and did not question this instinct...and that led to a large waste of time on my part.

11. Jul 29, 2014

### Staff: Mentor

I am a chemist. For me log means base 10, ln means base e.

Not that I am going to argue about this convention being the right one (even if it IS the right one ).

12. Jul 29, 2014

### symbolipoint

What is the typical practice for that application? What is the typical practice in business or industrial situations? What is the typical practice in academic situations? If you have found that application in your current schooling or academic work, then lesson instruction should make the implication clear for you.

13. Jul 29, 2014

### economicsnerd

If I'm reading math: $e$.
If I'm reading economics: $e$.
If I'm reading CS: $2$.

14. Jul 30, 2014

### NathanaelNolk

They also should use log10 in base 10. In my opinion, writing log(x) is okay and understandable, but still wrong.

15. Jun 27, 2015

### caters

Right because without a base as a subscript you don't know what the base is, whether it is base 2, base e, base 10, base 12, or even something like base 1/2 or base pi.

And if you don't know what the base is than how can you do the logarithm? It would be undefined without a base and even with some bases(like base 1 or any negative base).

Now if you had the radical or exponential equivalent of the logarithm then you could deduce from that what the base of the logarithm is.

16. Jun 28, 2015

### HallsofIvy

Staff Emeritus
As others have suggested, it depends upon the class. Generally speaking, in mathematics classes up to "PreCalculus" (I am tempted to say "pre-college") "log" generally means "log base 10". Past that, log base 10 is almost never used and "log" means natural logarithm.