Here's the "

proof" :(It's actually false, but

marginally so)

The

assertion
**log**_{2}x = log_{10}x + ln x
can be exactly replaced, using

logarithm properties by

**log**_{2}x = (log_{2}x/log_{2}10) + (log_{2}x/log_{2}e)
We will put both

rhs terms on the same

denominator giving

**log**_{2}x = log_{2}x(log_{2}e + log_{2}10)/(log_{2}e.log_{2}10)
in which we can

eliminate log_{2}x on each side and bring the denominator to the

lhs giving

**log**_{2}e.log_{2}10 = log_{2}e + log_{2}10
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