Originally Posted by

**DaGr8Gatzby** I was recently exposed to the following problem on my homework and I am stumped:

log(base 5)((sin(x))=-1/2

I have no idea how to proceed. This was my thought process working out the problem:

log(base b)(x) = y

b^y = x

Therefore:

5^(-1/2) = sin x

-sqrt(5) = sin x

$\displaystyle \textcolor{red}{5^{-\frac{1}{2}} = \frac{1}{\sqrt{5}} = \sin{x}}$

.... but I am at a loss to try and derive the number of possible answers from this answer. The interval is [0, 2pi). Thank you.