I posted the following in December 2021 on my first-year pure module's Piazza forum.
Hi everyone
I saw this a few years ago on QI, and found another version on the web at
http://mathandmultimedia.com/2014/12/02/merry-christmas-equation/
If we are told that
\(\qquad\displaystyle y=\frac{\ln(\frac{x}m-sa)}{r^2}\)
multiplying by \(r^2\) gives
\(\qquad yr^2=\ln(\frac{x}m-sa)\,.\)
Then taking \(e\) to the power of both sides give
\(\qquad\displaystyle e^{yr^2}=\frac{x}m-sa\,,\)
and multiplying both sides by \(m\) gives
\(\qquad me^{yr^2}=x-msa\,,\)
which can be rewritten as
\(\qquad me^{rry}=x-mas\,.\)
(And a Happy New Year!)
Best wishes,
Dr Feinstein
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