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

Multiplying both sides by , we have

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

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

.

Multiplying both sides of equation by , we have

.

Now, changing the exponent to the equivalent expression and changing the order of to (remember, multiplication is **commutative**), the final equation is

.

Interesting, isn’t it?

Merry Christmas and a prosperous new year to all. 🙂

Hi Guillermo,

This is a fun example! I have shared it on my blog as well and credited your site. Best wishes for a Happy Holiday season!

Shaun

Thanks. Happy holidays too Shaun.

This is wrong. If you follow your steps and multiply each side by m the m/1 and the x/m cancel each other out and you’re left with x – sa, no m. You gotta redo your equation.

When you multiply that side by m you do it like this:

m(x/m – sa) >> (xm/m – msa) you have to distribute the m all the way

THEN then m cancels and, after rearranging, you’re left with x-mas

What’s this equation known as?