If equation `6(log_(x)2-log_(4)x)+7=0` has roots `x_(1)` and `x_(2)` then `log_(2)x_(1)x_(2)` is equal to `(p)/(q)`, where p and q are co-prime numbers, then the value of `p+q` is equal to

If log_(sinx)(cos x) = (1)/(2) , where x in (0, (pi)/(2)) , then the value of sin x is equal to-

The expression log_(2)5-sum_(k=1)^(4)log_(2)(sin((k pi)/(5))) reduces to (p)/(q) where p and q are co-prime,the value of p^(2)+q^(2) is

If lim_(x rarr0)(x+ln(sqrt(x^(2)+1)-x))/(x^(3))=(p)/(q) where p and q are coprimes then find the value of |p^(2)-q^(2)|

If the quadratic equation x^(2)-px+q=0 where p, q are the prime numbers has integer solutions, then minimum value of p^(2)-q^(2) is equal to _________

If log_(b)a=3,log_(b)=-4. If the value of x satisfying theequation a^(3x)=c^(x)-1 is expressed in the form (p)/(q), where p and q are relatively prime then p+q is

If p, q are the roots of equation x^(2)+px+q=0, then value of p must be equal to

If 2 log_(8) N = p , log_(2) 2 N = q , and q - p = 4 , then the value of N is

If sum of all the solutions of the equation (4tan x+tan^(2)x+1)=2sqrt(2)sin(x+(pi)/(4))(1+tan^(2)x) in [0,pi] is (p, (pi)/(q)) where p,q are relatively prime number, then find the value of (p+q)

If the ratio of the coefficient of x^(10) in (1-x^(2))^(10) and term independent of x in (x-2/x)^(10) is p/q (where p and q are relative prime numbers) then q/8-p is