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