`Ifint_(log2)^x(dx)/(sqrt(e^x-1))=pi/6,"then " x " is equalto"` (a)4 (b) log 8 (c) log 4 (d) none of these

if int_(log2)^(x) (du)/(e^u-1)^(1/2) =pi/6 then e^x=

If y=(log)_(sinx)(tanx),t h e n(((dy)/(dx)))_(pi/4)"is equal to" (a) 4/(log2) (b) -4log2 (c) (-4)/(log2) (d) none of these

If (log)_k xdot(log)_5k=(log)_x5,k!=1,k >0, then x is equal to (a) k (b) 1/5 (c) 5 (d) none of these

If (log)_3{5+4(log)_3(x-1)}=2, then x is equal to 4 (b) 3 (c) 8 (d) (log)_2 16

(log)_(x-1)x (log)_(x-2)(x-1) (log)_(x-12)(x-11)=2,x is equal to: 9 (b) 16 (c) 25 (d) none of these

lim_(x->oo)[sqrt(x+sqrt(x+sqrt(x)))-sqrt(x)] is equal to (a)0 (b) 1/2 (c) log 2 (d) e^4

The value of 3^((log)_4 5)-5^((log)_4 3) is 0 (b) 1 (c) 2 (d) none of these

If x y^2=4a n d(log)_3((log)_2x)+(log)_(1/3)((log)_(1/2)y)=1 ,then x equals (a) 4 (b) 8 (c) 16 (d) 64

The differential coefficient of f((log)_e x) with respect to x , where f(x)=(log)_e x , is (a) x/((log)_e x) (b) 1/x(log)_e x (c) 1/(x(log)_e x) (d) none of these

If S={x in N :2+(log)_2sqrt(x+1)>1-(log)_(1/2)sqrt(4-x^2)} , then (a) S={1} (b) S=Z (d) S=N (d) none of these