[" If "u(x,y)=y log x+x log y," then "u_(x)u_(y)-],[log x-u_(y)log y+log x log y=],[(1)0],[(3)1]

If u(x,y)=y log x+x log y, then u_(x)u_(y)-u_(x)log x-u_(y)log y+log x log y=

if log (x+y) = log x + log y , then x= ____

If x ^( log y) = log x, then prove that (dy)/(dx) = (y)/(x) ((1- log x log y)/( (log x) ^(2)))

If log((x+y)/5) = 1/2 (log x + log y) , then show that x/y + y/x = 23 .

If x^(y)=y^(x) , prove that (dy)/(dx)=((y)/(x)-log y)/((x)/(y)-log x)

If "log"_(y) x = "log"_(z)y = "log"_(x)z , then

If "log"_(y) x = "log"_(z)y = "log"_(x)z , then

If log_y x +log_x y=7, then the value of (log_y x)^2+(log_x y)^2, is

State, true or false : (i) log 1 xx log 1000 = 0 (ii) (log x)/(log y) = log x - log y (iii) If (log 25)/(log 5) = log x , then x = 2 (iv) log x xx log y = log x + log y