[ prove x^(log y)-log z]

prove that x^(log y-log z)*y^(log z-log x)*z^(log x-log y)=1

Find the value of (x^(log y - log z))(y^(log z-log x))(z^(log x - log y))

Prove that x^(log y - logz) xx y^(log z - logx) xx z^(log x - log y) = 1 .

Suppose x;y;zgt0 and are not equal to 1 and log x+log y+log z=0 . Find the value of x^(1/log y+1/log z)xx y^(1/log z+1/log x)xx z^(1/logx+1/logy) (base 10)

Suppose x,y,z>1 then least value of log(xyz)[(log x)/(log y log z)+(log y)/(log x log z)+(log z)/(log x log y)]

Delta=|[log x ,log y, log z],[log 2 x, log 2 y, log 2 z],[log 3 x, log 3 y, log 3 z ]|=

If (log x)/(y-z) = (log y)/(z-x) = (log z)/(x-y) , then prove that xyz = 1 .

If (log x)/(b-c) = (log y)/(c-a) = (log z)/(a-b) , then prove that x^(b+c).y^(c+a).z^(a+b) = 1