I am currently taking a course in differential equations and got back the results of my first exam. I was surprised to see that I had points taken off for writing the natural logarithm of $x$ as $\log(x)$ instead of $\ln(x)$.
Is the notation $\log(x)$ for the natural log of $x$ incorrect? I was under the impression that it is not uncommon for mathematicians to write the natural logarithm in this way.
Best Answer
It's normally context-dependent. To a mathematician, $\log(x)$ means $\log_{10}(x)$, and the natural log is always $\ln(x)$. To a physicist, $\log(x)$ is the natural logarithm. To an engineer (not computer), $\log(x)=\log_{10}(x)$. To a computer engineer, $\log(x)=\log_2(x)$.
Bottom line: if you want to be completely unambiguous, and you're not sure of the context, write $\log_b(x)$, where $b=e, 2,$ or $10$. On the other hand, $\ln(x)$ always means $\log_e(x)$, so that's also unambiguous.