If `log x=2 log (x+k)` where `x in R^+` and kis a positive real number then true act of values of `k` is

If log x=2log(x+k) where x in R^(+) and kis a positive real number then true act of values of k is

If log_(10)(x^(3)+y^(3))-log_(10)(x^(2)+y^(2)-xy)<=2, where x,y are positive real number,then find the maximum value of xy.

Let the function ln f(x) is defined where f(x) exists for 2 geq x and k is fixed positive real numbers prove that if -k f(x) geq d/(dx) (x.f(x)) then f(x) geq Ax^(-k-1) where A is independent of x.

Let the function ln f(x) is defined where f(x) exists for 2 geq x and k is fixed positive real numbers prove that if -k f(x) geq d/(dx) (x.f(x)) then f(x) geq Ax^(k-1) where A is independent of x.

Let the function ln f(x) is defined where f(x) exists for x geq 2 and k is fixed positive real numbers prove that if d/(dx) (x.f(x)) geq -k f(x) then f(x) geq Ax^(-1-k) where A is independent of x.

Let the function ln f(x) is defined where f(x) exists for x>=2 and k is fixed positive real numbers prove that if (d)/(dx)(x.f(x))>=-kf(x) then f(x)>=Ax^(-1-k) where A is independent of x

If (log)_(10)(x^3+y^3)-(log)_(10)(x^2+y^2-x y)lt=2, and x ,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-x y)lt=2, and x ,y are positive real number, then find the maximum value of x ydot

Consider the equation log_(10)(x+pi)=log_(10)(x)+log_(10)(pi), where xis a positive real number.This equations has-

If t=(ln k)/(y)+ln((k)/(y))+(ln ky)+(ln k)y (where k is a positive constant and k<1,y in R), then the least value of t ' is -