Verified answer

a) f(g(x))

for f(x)=log x x must be >0

so sin(X)>0 => x must be from the domanin (0,pi)+2k*pi for every k from Z

sin x<1 =>log(sin(X)) will take values in (-infinit, 0)

b) g(f(x))

f(x)= log x =>x>0

sin has no restrictions

sin takes values in [0,2*pi]

c) f(f(g(x)))

first sin x>0 => a)

second log(base 2)sin(x)>0

=> sin x>1 which cannot be. therefor there is no domain for this one

See my answer to the same question asked by Sita about 9 hours before yours.