`log(1/2)+log (2/3)+log(3/4) +….+ log(99/100)` = ______

log_(2)1. log_(3)2. log_4)3.log_(5)4.log_(6)5……. Log_(200)199 = ______

The number N=2^(log_(2)3log_(3)4*log_(4)5.......log_(99)100) simplifies to

The value of |[log _(3) 512 , log _(4) 3 ],[ log _(3) 8 , log _(4) 9]||[log _(2) 3 , log _(8) 3],[ log _(3) 4 , log _(3) 4]| is

Which of the following when simplified, vanishes? a. 1/((log)_3 2)+2/((log)_9 4)-3/((log)_(27)8) b. (log)_2(2/3)+(log)_4(9/4) c. -(log)_8(log)_4(log)_2 16 d. (log)_(10)cot1^0+\ (log)_(10)cot2^0+(log)_(10)cot3^0++(log)_(10)cot89^0

If "log"_(2) a + "log"_(4) b + "log"_(4) c = 2 "log"_(9) a + "log"_(3) b + "log"_(9) c = 2 "log"_(16) a + "log"_(16) b + "log"_(4) c =2 , then

If "log"_(2) a + "log"_(4) b + "log"_(4) c = 2 "log"_(9) a + "log"_(3) b + "log"_(9) c = 2 "log"_(16) a + "log"_(16) b + "log"_(4) c =2 , then

int_0^(pi//2)(cosx)/((2+sinx)(1+sinx))dx equals (a) log(2/3) (b) log(3/2) (c) log(3/4) (d) log(4/3)

lim_(x rarr 3) (log(2x-3)-log(3x + 2))/(log(2x +1))= _______.

Prove log a + log a^(2) + "log" a^(3) +……..+ log a^(n) = (n (n + 1))/(2) log a