Let `x` be a positive real number such that `sin(arctan\ (x)/(2))=(x)/(3)`. The value of `(log_(5)x)` is equal to

Suppose that beta is a real number such that 3^(2x +3) = (3^(x))/(2^(x)) , then the value of 2^(-(1+log_(2)3)beta) is equal to

Suppose that beta is a real number such that 3^(2x +3) = (3^(x))/(2^(x)) , then the value of 2^(-(1+log_(2)3)beta) is equal to (A) 6 (B) 9 (C) 18 (D) 27

Let x,y,z be positive real numbers such that log_(2x)z=3,log_(5y)z=6 and log_(xy)z=(2)/(3) then the value of z is

If a positive real number x satisfy the condition x^(5)-x^(3)+ x=1 then the minimum value of x^(6) is equal to

Let f be a real - valued function defined on R ( the set of real numbers) such that f(x) = sin^(-1) ( sin x) + cos^(-1) ( cos x) The value of f(10) is equal to

Let f be a real - valued function defined on R ( the set of real numbers) such that f(x) = sin^(-1) ( sin x) + cos^(-1) ( cos x) The value of f(10) is equal to

Let f be a real - valued function defined on R ( the set of real numbers) such that f(x) = sin^(-1) ( sin x) + cos^(-1) ( cos x) The value of f(10) is equal to

Let x,y,z be positive real numbers such that log_(2x)z=3, log_(5y)z=6 and log_(xy)z=2/3 then the value of z is