If x=2,y=3,m=1 and n=4,find the value of `(x^(m+n)y^(m-n))/(x^(m-n)y^(m+n))`

Given log x = 2m - n, log y = n - 2m and log z = 3m - 2n, find in terms of m and n, the value of "log" (x^(2)y^(3))/(z^(4)) .

If x and y vary inversely, find the values of l, m and n :

If x and y vary inversely, find the values of l, m and n :

If x = (12 mn)/( m +n) , fnd the value of : (x + 6m)/(x - 6m) + (x + 6n)/(x - 6n)

Find the value of the products: (3m-2n)(2m-3n)a t\ m=1,\ n=-1

Let m and n be positive integers and x,y gt 0 and x+y =k, where k is constant. Let f (x,y) = x ^(m)y ^(n), then: (a) f (x,y) is maximum when x= (mk)/(m+n) (b) f (x,y) is maximuim where x =y (c) maximum value of f (x,y) is (m^(n)n ^(m) k ^(m+n))/((m+n)^(m+n)) (d) maximum value of f (x,y) is (k ^(m+n) m ^(m)n ^(n))/((m+n)^(m+n))

Let log x= 2m - 3n and log y = 3n - 2m Find the value of log (x^(3) /y ^(2)) in terms of m and n.

Let x, y be positive real numbers and m, n be positive integers, The maximum value of the expression (x^(m)y^(n))/((1+x^(2m))(1+y^(2n))) is

If m,n in N and m=(n^2-n-35)/(n-4) , then find the value of m.

If x,y are positive real numbers and m, n are positive integers, then prove that (x^(n) y^(m))/((1 + x^(2n))(1 + y^(2m))) le (1)/(4)