Prove that
(v) `1/(log_(xy)(xyz)) + 1/(log_(yz)(xyz)) + 1/(log_(zx)(xyz)) = 2`

Evaluate (1)/(log_(xy)(xyz))+(1)/(log_(yz)(xyz))+(1)/(log_(zx)(xyz))

The value of [(1)/(log_(xy)(xyz))+(1)/(log_(yz)(xyz))+(1)/(log_(zx)(xyz))] is equal to

Let L denots value of cos^(2)(alpha - beta) if sin2alpha + sin2beta = (1)/(2), cos2alpha + cos2beta = (sqrt(3))/(2) and M denotes value of (1)/(log_(xy)xyz) + (1)/(log_(yz)xyz) + (1)/(log_(zx)xyz) then 16L^(2) + M^(2) is

Let L denots value of cos^(2)(alpha - beta) if sin2alpha + sin2beta = (1)/(2), cos2alpha + cos2beta = (sqrt(3))/(2) and M denotes value of (1)/(log_(xy)xyz) + (1)/(log_(yz)xyz) + (1)/(log_(zx)xyz) then 16L^(2) + M^(2) is

Prove that : (iii) (yz)^(log(y/z))(zx)^(log(z/x))(xy)^(log(x/y)) = 1

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

Solve: log_(a)x log_(a)(xyz)=48log_(a)y log_(a)(xyz)=12;log_(a)z log_(a)(xyz)=84

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

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

If log_(xyz)x + log_(xyz)y + log_(xyz)z= log_(10)p , then p = ______.