the value of sinx varies regularly.
So, graph needs to be analyzwd in intervals.
first thing is that:  log(x) is defined for x>0.
So, sinx>0.
first take interval : 0<x<=pi/2.
sinx is an increasing function for this period and logx is an increasing function.
So, log(sinx) will also increase.
log1 = 0 so, log (sin(pi2))=0.
log(m) is negative when 0<m<1.
So, break it into the intervals and draw the graph.
Note: keep in mind the domain of sinx.