ln(x) ~ 10 * [log15(x) – log41(x)], which is only off by a factor of 0.000131 …

But that’s not nearly as cool.

]]>Even more cool (to me) is the fact that there are no other approximations of this kind — since 2 is the only integer for which ln(2) is less than 1, it’s the only one that can generate a difference of ~ 1 between 1/ln(r) and 1/ln(k) for integers r and k.

]]>ln x ~ lg x – log x

e.g.

ln 1024 ~ lg 1024 – log 1024 ~10 – 3 ~ 7 — is close to the actual 6.931471805599453

]]>Thanks so far and best regards from Germany

PS.: Great site with a lot of amazing math stuff. Please keep it up!

]]>More explicitly, log_{2} x ≈ log_{e} x + log_{10} x.

“lg” is the short form for “log base 1o” and not “base 2”.

But afaik “log base 2” has the short form “ld x” or “lb x”!? ]]>