If `(log)_4 5=aa n d(log)_5 6=b ,` then `(log)_3 2` is equal to `1/(2a+1)` (b) `1/(2b+1)` (c) `2a b+1` (d) `1/(2a b-1)`

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 (a+(log)_4 3)/(a+(log)_2 3)=(a+(log)_8 3)/(a+(log)_4 3)=b ,then b is equal to 1/2 (2) 2/3 (c) 1/3 (d) 3/2

If (log)_(10)5=aa n d(log)_(10)3=b ,t h e n (A) (log)_(30)8=(3(1-a))/(b+1) (B) (log)_(40)15=(a+b)/(3-2a) (C) (log)_(243)32=(1-a)/b (d) none of these

If (log)_(10)2=a ,(log)_(10)3=bt h e n(log)_(0. 72)(9. 6) in terms of a and b is equal to (a) (2a+3b-1)/(5a+b-2) (b) (5a+b-1)/(3a+2b-2) (c) (3a+b-2)/(2a+3b-1) (d) (2a+5b-2)/(3a+b-1)

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

If b >1,sint >0,cost >0a n d(log)_b(sint)=x ,t h e n(log)_b(cost) is equal to (a) 1/2(log)_b(1-b^(2x)) (b) 2log(1-b^(x/2)) (log)_bsqrt(1-b^(2x)) (d) sqrt(1-x^2)

If sin^(-1)((2a)/(1+a^2))+sin^(-1)((2b)/(1+b^2))=2tan^(-1)x , then x is equal to [a , b , in (0,1)] (a) (a-b)/(1+a b) (b) b/(1+a b) (c) b/(1+a b) (d) (a+b)/(1-a b)

If the third term in expansion of (1+x^(log_2x))^5 is 2560 then x is equal to (a) 2sqrt2 (b) 1/8 (c) 1/4 (d) 4sqrt2

If p >1 and q >1 are such that log(p+q)=logp+logq , then the value of log(p-1)+log(q-1) is equal to (a) 0 (b) 1 (c) 2 (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