Show that `a^(log_(a^2)^(x))xxb^(log_(b^2)^(y))xxc^(log_(c^2)^(z))=sqrt(xyz)`

Prove that : (iv) a^(log_(a^2)x) xx b^(log_(b^2)y) xx c^(log_(c^2)z) = sqrt(xyz)

If a,b,c are in A.P and x,y,z are in G.P then prove that a^((b-c)log_(a)^(x))xxb^((c-a)log_(b)^(y))xxc^((a-b)log_(c )^(z))=1

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

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)

If log x(log x)/(a^(2)+ab+b^(2))=(log y)/(b^(2)+bc+c^(2))=(log z)/(c^(2)+ca+a^(2)) then x^(a-b)*y^(b-c)*z^(c-a)=

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

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

The value of the determinant ,log_(a)((x)/(y)),log_(a)((y)/(z)),log_(a)((z)/(x))log_(b)((y)/(z)),log_(b)((z)/(x)),log_(b)((x)/(y))log_(c)((z)/(x)),log_(c)((x)/(y)),log_(c)((y)/(z))]|

If (log_(e)x)/(y-z)=(log_(e)y)/(z-x)=(log_(e)z)/(x-y), prove that xyz=1

Solve the system of equations : log_(a)(x)log_(a)(xyz)=48log_(a)(y)log_(a)(xyz)=12log_(a)(z)log_(a)(xyz)=84,quad a>0,a!=1