If `(tan(ln6)dottan(ln2)dot"tan"(ln3))/(tan(ln6)-tan(ln2)-"tan"(ln3))=k ,` then the value of `k` is________

If A=((log _(2) 3)^(3)-(log _(2) 6)^(3)-(log _(2) 12)^(3)+(log _(2) 24)^(3))/(6) then the value of (2^(A)) is equal to

(cosec x)/(log ("tan"(x)/(2)))

If int(tan^(9)x)dx=f(x)+log|cosx|, where f(x) is a polynomial of degree n in tan x, then the value of n is

If (log)_a b=2,(log)_b c=2,a n d(log)_3c=3+(log)_3a , then the value of c//(a b) is............

(log x)/( (1 + log x)^(2))

If log ((x+y)/3)=1/2 (log x +log y) then find the value of x/y+y/x

The x , y , z are positive real numbers such that (log)_(2x)z=3,(log)_(5y)z=6,a n d(log)_(x y)z=2/3, then the value of (1/(2z)) is ............

If f(x)=(tan(pi/4+(log)_e x))^((log)_x e) is to be made continuous at x=1, then what is the value of f(1)?

If (log)_(12)27=a , then find (log)_6 16 interms of a

If (log)_a3=2 and (log)_b8=3 , then prove that (log)_a b=(log)_3 4.