If log x=a,log y=b,and log z=c then log x^2y[numertr]/sqrt of z[denom] is equivalent to?:

options:
a.a^a+b-1/2c
b.2ab-1/2c
c.42a+b+1/2c
d.2a+b-1/2c

d.2a+b-1/2c because:
Hint 1: log(mn) = logm + logn
Hint 2: log(m/n) = logm - logn
Hint 3: log(m^n) = n logm
Hint 4: √m = m^(1/2)

A = log[x²y/√z]
A = logx² + logy - log√z : Hint1 , Hint2
A = 2logx + logy - logz^(1/2) : Hint3 , Hint4
A = 2logx + logy - 1/2 logz
A = 2a + b - 1/2c