TITLE: What does $\lg x$ mean? is it $\log_2 x$ or $\log_{10} x$ in binary trees
QUESTION [12 upvotes]: I'm a bit confused, $\log_{10} x = \log x $ right? I believe I've read somewhere that $\log_{2} x = \lg x$ but some people say $\lg = \log$.
So what does $\lg$ really stand for? specifically when talking about "binary trees"

REPLY [2 votes]: The ISO 80000 specification, published in 2019, tries to resolve the numerous ambiguities in the notations for logarithms. It recommends the following notations:
$\lg x\equiv\log_{10}x\\
\ln x\equiv\log_e x\\
{\rm lb}\, x\equiv\log_2 x$.
These ISO recommendations try to avoid the ambiguity in the notations for the common logarithm ${\rm Log}\,  x\equiv\log x\equiv\log_{10} x$, as the same notation is sometimes used for the natural logarithm $\log x\equiv\ln x\equiv\log_e x$. The ISO rules also discourage the use of ${\rm lg}\, x\equiv\log_2 x$. See a discussion of the ambiguities HERE.