Take the square root of both
sides. Take the cosecent of both sides. Raise both sides to the -th power. Take
a logarithm of both sides.

Check out this dialogue between two calculus students (based on a true story):

- Devyn
- Riley, I’ve been thinking about the interest on my bank account.
- Riley
- So, like the compound interest formula,
- Devyn
- Yes! To make it easier to work with, suppose I deposit just $1, so .
- Riley
- A $1 bank account balance? I can imagine that!
- Devyn
- If the interest is compounded monthly, , and if the deposit is at interest, then .
- Riley
- Since , that brings you to
- Devyn
- My question is: How long does it take the account to double in value? How long until the account balance is $2?
- Riley
- Can’t we just setup
- Devyn
- Of course, but how to solve that for ? The variable is up in an exponent.
- Riley
- Hmmmm. I’m not sure…

What kind of operation will allow us to solve for ?