log2(x) = log10(x) + ln(x) (idea)

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

4.7646=4.7925

Which is 99.418 % accurate