lg x ≈ ln x + log10 x.
In words, log base 2 is approximately natural log plus log base 10. It’s a pleasant coincidence that there’s a simple relationship between the three most commonly used logarithms.
Knuth credits the approximation to R. W. Hamming and notes that the relative error is less than 1%. In fact, it’s easy to show that the relative error is exactly equal to
1 – (1 + 1/ln 10) ln 2 ≈ 0.0058
for all x.
Related post: The most interesting logs in the world