I need to solve 2sin(eˆ(x/4))+1=0 for x

My attempted solution:

sin(eˆx/4) = -.5

arcsin(-.5) = eˆ(x/4)

ˆ

I understand why this is where I went wrong;

because eˆ(x/4) is never negative, but I don't understand how I would solve this equation, and more importantly I don't understand why I couldn't use inverse trig functions to solve this problem.I thought that if sin x = y then arcsiny = x