Here's the "proof" :(It's actually false, but marginally so)

The assertion

log2x = log10x + ln x

can be exactly replaced, using logarithm properties by

log2x = (log2x/log210) + (log2x/log2e)

We will put both rhs terms on the same denominator giving

log2x = log2x(log2e + log210)/(log2e.log210)

in which we can eliminate log2x on each side and bring the denominator to the lhs giving

log2e.log210 = log2e + log210

Miracle ! we now have nothing but constants and can use any pocket calculator or GNU Octave - as I did - to finish the proof: this translates as


Which is 99.418 % accurate