log_(z^(2))x^(2)y^(2)=?

if x^(4) -y^(4)-x^(2)y^(2)-2xy^(3)= z^(6) then prove that log_(z)(x^(2) -y^(2)-xy) + log_(z) (x^(2) +y^(2) +xy) =6

If log x log y log z=(y-z)(z-x)(x-y) then a )x^(y)*y^(z)*z^(x)=1 b) x^(2)y^(2)z^(2)=1c)root(z)(x)*root(y)(y)*root(z)(z)1=d) None of these

Let x,y and z be positive real numbers such that x^(log_(2)7)=8,y^(log_(3)5)=81 and z^(log_(5)216)=(5)^((1)/(3)) The value of (x(log_(2)7)^(2))+(y^(log_(3)5)^^2)+z^((log_(5)16)^(2)), is

Calculate : log_(x^2)x xx log_(y^2)y xx log_(z^2)z

What is the value of log_(y)x^(5)log_(x)y^(2)log_(z)z^(3) ?

3^(x)+3^(y)+3^(z)+3^(t)=24,log_(z)x+log_(z)t=y,(x)/(x^(4)+y^(2))+(y)/(x^(2)+y^(4))=(1)/(xy)

For the system of equation "log"_(10) (x^(3)-x^(2)) = "log"_(5)y^(2) "log"_(10)(y^(3)-y^(2)) = "log"_(5) z^(2) "log"_(10)(z^(3)-z^(2)) = "log"_(5)x^(2) Which of the following is/are true?

For the system of equation "log"_(10) (x^(3)-x^(2)) = "log"_(5)y^(2) "log"_(10)(y^(3)-y^(2)) = "log"_(5) z^(2) "log"_(10)(z^(3)-z^(2)) = "log"_(5)x^(2) Which of the following is/are true?

a=y^(2),b=z^(2),c=x^(2) then prove that log_(a)x^(3)*log_(b)y^(3)*log_(c)z^(3)=(27)/(8)