Is this festive picture a valid equation?

Question

Ive seen this picture floating around, and I was wondering if it was a legitimate mathematical equation, or if it just looks convincing enough to fool Luddites like myself?

Answer 1

They're correct (with a few caveats that others have pointed out).

The manipulations:

1. Original equation
2. Multiply both sides by $r^2$
3. Exponentiate both sides (make each side the exponent base $e$). The exponent doesn't show up on the right side because $e^{\log_e(f(x))} = f(x)$.
4. Multiply both sides by $m$.
5. Write out $r^2$ as $rr$ (both mean $r \cdot r$) and $msa$ as $mas$ and $yrr$ as $rry$ (valid by commutative property of multiplication).