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

.... 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.