# Solving the Merry Christmas Equation

It’s December again and many people are celebrating Christmas. Here in Japan, Christmas is also celebrated even though only less than 1% of the population are Christians.

Anyway, I will be very busy this month, but let’s start our month with solving an equation that will lead to Merry Christmas. Sound confusing? Let’s start.

To understand the solution below, it would help if you have some prior knowledge of about natural logarithms.

The Christmas Equation

Let’s solve the equation $y = \displaystyle \frac{ \ln (\frac{x}{m} - sa)}{r^2}$

Multiplying both sides by $r^2$, we have $yr^2 = \displaystyle \ln (\frac{x}{m} - sa)$

Now, to eliminate the natural logarithm, we use the equation as powers of the rational number $e$. That is

$e^{yr^2} = \displaystyle e^{\ln (\frac{x}{m} - sa)}$

Since $e$ and $\ln$ are inverses of each other, the only expression left on the right hand sides of the equation is the expression inside the parenthesis. So,

$e^{yr^2} = \displaystyle \frac{x}{m} - sa$.

Multiplying both sides of equation by $m$, we have

$me^{yr^2} = \displaystyle x - sam$.

Now, changing the exponent $yr^2$ to the equivalent expression $rry$ and changing the order of $sam$ to $mas$ (remember, multiplication is commutative), the final equation is

$me^{rry} = x-mas$.

Interesting, isn’t it?

Merry Christmas and a prosperous new year to all. 🙂