Let `x= 2^(log 3)` and `y=3^(log 2)` where base of the logarithm is 10,then which one of the following holds good. (A) `2x lt y` (B) `2y lt x` (C) `3x = 2y` (D) `y = x`.

(2x) ^ (ln2) = (3y) ^ (ln3) 3 ^ (ln x) = 2 ^ (ln y)

If log(xy^(3))=1 and log(x^(2)y)=1, then the value of xy is equal to (where base of the logarithm is 32)

Express each of the following in a form free from logarithm : (i) 2 log x - log y = 1 (ii) 2 log x + 3 log y = log a (iii) a log x - b log y = 2 log 3

If a function is represented parametrically be the equations x=(1+(log)_e t)/(t^2); y=(3+2(log)_e t)/t , then which of the following statements are true? (a) y^('')(x-2x y^(prime))=y (b) y y^(prime)=2x(y^(prime))^2+1 (c) x y^(prime)=2y(y^(prime))^2+2 (d) y^('')(y-4x y^(prime))=(y^(prime))^2

If a function is represented parametrically be the equations x=(1+(log)_e t)/(t^2); y=(3+2(log)_e t)/t , then which of the following statements are true? (a) y^('')(x-2x y^(prime))=y (b) y y^(prime)=2x(y^(prime))^2+1 (c) x y^(prime)=2y(y^(prime))^2+2 (d) y^('')(y-4x y^(prime))=(y^(prime))^2

Let (x_(0),y_(0)) be the solution of the following equations In (2x)^(In2)=(3y)^(ln3) and 3^(ln x)=2^(ln y) Then x_(0) is

If a^(2) = log x, b^(3) = log y and 3a^(2) - 2b^(3) = 6 log z , express y in terms of x and z.

Let (x_(0),y_(0)) be the solution of the following equations: (2x)^(ln2)=(3y)^(ln3) and 3^(ln x)=2^(ln y) Then value of x_(0) is: