we are given
[tex] log(z^3\sqrt{x^5y} ) [/tex]
step-1: Firstly , we will expand log terms by using property
[tex] log(a*b)=log(a)+log(b) [/tex]
[tex] log(z^3)+log(\sqrt{x^5y} ) [/tex]
step-2: Now, we can bring exponent in front
[tex] log(a^n)=n*log(a) [/tex]
[tex] =log(z^3)+log(x^5y)^{\frac{1}{2}} [/tex]
[tex] =3log(z)+\frac{1}{2}log(x^5y) [/tex]
step-3: we can again expand second term
[tex] =3log(z)+\frac{1}{2}(log(x^5)+log(y)) [/tex]
[tex] =3log(z)+\frac{1}{2}(5log(x)+log(y)) [/tex]
so, we will get
[tex] =3log(z)+\frac{1}{2}(5log(x)+log(y)) [/tex]...............Answer
