What does lg x mean? is it $\log_2 x$ or $\log_{10} x$ in binary trees

Question

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"

There are many different notations. In the context of binary trees, you'd probably talk about $\log_2$, but I've seen it marked as $\log$, $\log_2$ or $\lg$.
Almost certainly $\log_2$ $-$ the hint is in the word 'binary'!

George V. Williams · Answer 1 · 2013-01-19 16:05:02Z

up vote 3 down vote

$\lg$ will usually stand for $\log_2$ when talking about binary. In Germany and Russia, $\lg$ refers to $\log_{10}$. Source

answered Jan 19 at 16:05

George V. Williams
2,166525

Asaf Karagila · Answer 2 · 2013-01-19 16:07:09Z

up vote 0 down vote

It is common that $\lg=\log_2$, but note that $\log_a = \Theta(\log_b)$, because $$\log_a x = \frac{\log_b x}{\log_b a}.$$

answered Jan 19 at 16:07

Asaf Karagila
90.8k12136283

2 Answers