`int_2^4 log[x]dx` is (A) `log2` (B) `log3` (C) `log5` (D) none of these

If 2^(x+y)=6^ya n d3^(x-1)=2^(y+1), then the value of (log3-log2)(x-y) is 1 (b) (log)_2 3- (log)_3 2 (c) log(3/2) (d) none of these

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

The value of the integral int_0^oo(xlogx)/((1+x^2)^2)dx ,is (a)0 (b) log 7 (c) 5 log 13 (d) none of these

The value of the integral int_0^oo(xlogx)/((1+x^2)^2)dx (a) 0 (b) log 7 (c) 5 log 13 (d) none of these

int_0^1 log(sqrt(1+x)+sqrt(1-x))dx= (A) 1/2(log2-pi/2+1) (B) 1/2(log2+pi/2+1) (C) 1/2(log2+pi/2-1) (D) none of these

Q. If log_x a, a^(x/2) and log_b x are in G.P. then x is equal to (1) log_a(log_b a) (2) log_a(log_e a)+log_a log_b b (3) -log_a(log_a b) (4) none of these

If x, y, z are in G.P. and a^x=b^y=c^z , then (a) logba=log_ac (b) log_cb =log_ac (c) log_ba=log_cb (d) none of these

int(log_e(x+1)-log_ex)/(x(x+1))dx is equal to (A) -1/2[log(x+1)^2-1/2logx]^2+log_e(x+1)log_ex+C (B) -[(log_e(x+1)-log_ex]^2 (C) c-1/2(log(1+1/x))^2 (D) none of these

If a ,b ,c ,d in R^+-{1}, then the minimum value of (log)_d a+(log)_b d+(log)_a c+(log)_c b is (a) 4 (b) 2 (c) 1 (d)none of these

(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