Binary Logarithm - Using Calculators

Using Calculators

An easy way to calculate the log₂(n) on calculators that do not have a log₂-function is to use the natural logarithm "ln" or the common logarithm "log" functions, which are found on most "scientific calculators". The specific change of logarithm base formulae for this are:

log₂(n) = ln(n)/ln(2) = log(n)/log(2)

so

log₂(n) = log_e(n)×1.442695... = log₁₀(n)×3.321928...

and this produces the curiosity that log₂(n) is within 0.6% of log_e(n) + log₁₀(n). log_e(n)+log₁₀(n) is actually log_2.0081359...(n) where the base is e1/(1+log₁₀e) = 101/(1 + log_e10) ≈ 2.00813 59293 46243 95422 87563 25191 0 to (32 significant figures). Of course, log₁₀10 = log_ee = 1.