(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

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

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)=48(log)_(a)y log_(a)(xyz)=12,backslash a>0,backslash a!=1(log)_(a)z log_(a)(xyz)=84

det[[log_(x)xyz,log_(x)y,log_(x)zlog_(y)xyz,1,log_(y)zlog_(z)xyz,log_(z)y,1]]=0

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

Positive numbers x,y backslash and backslash z satisfy xyz:)=(:10^(1) and (log_(10)x)*(log_(10)yz)+(log_(10)y)*(log_(10)z)=468. Find the value of (log_(10)x)^(2)+(log_(10)y)^(2)+(log_(10)z)^(2)