Prove that `yz^(log frac{y}{z}) *(zx)^(log frac{z}{x})* (xy)^(log frac{x}{y}) =1`

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

The value of (yz)^(log y-log z)xx(zx)^(log z-log x)xx(xy)^(log x-log y) is

(log a)/(y-z)=(log b)/(z-x)=(log c)/(x-y) then value of abc=

If m is the geometric mean of ((y)/(z))^(log(yz)),((z)/(x))^(log(zx))"and"((x)/(y))^(log(xy)) then what is the value of m?

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

(log a)/(y-z)=(log b)/(z-x)=(log c)/(x-y), thena ^(x)b^(y)c^(z) is

If the shortest distance between the lines frac{x - lambda} {-2} = frac{y - 2} {1} = frac{z - 1} {1} and frac{x - sqrt 3}{1} = frac{y-1}{-2} = frac{z-2}{1} is 1, then the sum of all possible values of lambda is :