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I was always taught that "log" is log base ten and "ln" is log base $e$, and there are plenty of sources that use this. But a lot of other sources use "log" as the natural log, and some books I have don't seem to specify which system they use and I can't quite figure it out sometimes. Is there a good way to know when somebody is using one or the other, or are there particular fields which tend to use one system or the other?

Vedvart1
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    Read the ingredients on the label. Usually it says organic or something similar, otherwise you can't assume it is entirely natural. – copper.hat Apr 23 '17 at 04:01
  • More seriously; the two $\log,\ln$ are often used interchangeable. Sometimes a base is specified as in $\log_b$. Text books in secondary schools used to use $\log$ for $\log_{10}$. – copper.hat Apr 23 '17 at 04:03
  • In most purely mathematical contexts at a level higher than introductory calculus, $\log$ will mean the natural logarithm. In science and engineering, this is less likely. The ISO 31-11 standard, which defines "mathematical signs and symbols for use in physical sciences and technology" according to Wikipedia, requires the use of $\ln$ and $\lg$. I don't know to what extent this practice is observed. – user49640 Apr 23 '17 at 04:08
  • If they ever make a claim like $\frac { log x}{dx}= \log x $ or $\int \frac 1/x dx=\log x$ they mean natural log. It is, surprisingly, actually not that important. Un natural log results are exactly the same as natural log results but with a conversion, factor. – fleablood Apr 23 '17 at 04:38

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Just look for instances that give away which log they are referring to.

If you are using a precalc or a calc textbook, the chances that log refer to base 10 is slim to none.

Saketh Malyala
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    Often times, precalculus textbooks use $\log$ to mean log base 10. Calculus textbooks almost never use "log" and opt instead for $\ln$, for better or worse. – Cameron Williams Apr 23 '17 at 04:05
  • Out of curiosity, why is there a discrepancy? What was it originally, and when did the usage change and why? – Vedvart1 Apr 23 '17 at 04:07
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    I disagree with this, simply because most of the textbooks I've used in both tutoring in different environments and teaching use $\ln$ to denote the logarithm of base $e$. However, it is a good idea to use context to differentiate the two. If it's a higher-level math text book, then $\log$ is much more common to see. However, if it is a textbook used by scientists and engineers, you are more likely to see $\ln$. – Decaf-Math Apr 23 '17 at 04:07