If `(log)_(10)(x^3+y^3)-(log)_(10)(x^2+y^2-x y)lt=2,w h e r ex ,y` are positive real number, then find the maximum value of `x ydot`

If log_(10)(x^(3)+y^(3))-log_(10)(x^(2)+y^(2)-xy) =0,y>=0 is

If x and y are positive real numbers such that x^(2)y^(3)=32 then the least value of 2x+3y is

If log_(10)|x^(3)+y^(3)|-log_(10)|x^(2)-xy+y^(2)|+log_(10)|x^(3)-y^(3)|-log_(10)|x^(2)+xy+y^(2)|=log_(10)221 . Where x, y are integers, then Q. If y=2 , then value of x can be :

If log_(10)x+log_(10)y=2, x-y=15 then :

If 3 log_(10) (x^(2) y) = 4 + 2 log_(10) x - log_(10) y , where x and y are both + ve, and x - y = 2 sqrt(6) , then the value of x is

If x , y >0,(log)_y x+(log)_x y=(10)/3 a n d x y=144 , t h e n(x+y)/2=sqrt("N")" w h e r e N" is a natural number, find the value of Ndot

If log_(10)x^(2) -log_(10)sqrt(y) =1 , find the value of y, when x=2

If log_(10)|x^3 + y^3|-log_(10) |x^2-xy + y^2|+log_(10)|x^3-y^3|-log_(10)|x^2+xy+y^2|=log_(10)221. wherex, y are integers , then (i) if x=111 then y can be: (ii) if y=2then value of x can be:

If "log"_(10) x =y, " then log"_(10^(3))x^(2) equals

If x and y are positive real numbers such that 2log(2y - 3x) = log x + log y," then find the value of " x/y .