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"
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$\begingroup$$\lg$ will usually stand for $\log_2$ when talking about binary. In Germany and Russia, $\lg$ refers to $\log_{10}$. Source
$\endgroup$ 1 $\begingroup$It is common that $\lg=\log_2$, but note that $\log_a = \Theta(\log_b)$, because $$\log_a x = \frac{\log_b x}{\log_b a}.$$
$\endgroup$ 1 $\begingroup$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.
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