(i) `1/log_3 2 + 2/log_9 4 + 3 /log_27 8`=

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

Find x if 9^(1//log_(2)3) le log_(2) x le log_(8) 27

Find the value of 81^((1//log_5 3))+(27^(log_9 36)) + 3^((4/(log_7 9))

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

Comprehension 2 In comparison of two numbers, logarithm of smaller number is smaller, if base of the logarithm is greater than one. Logarithm of smaller number is larger, if base of logarithm is in between zero and one. For example log_2 4 is smaller than (log)_2 8\ a n d(log)_(1/2)4 is larger than (log)_(1/2)8. Identify the correct order: (log)_2 6 (log)_3 8> log_3 6>(log)_4 6 (log)_3 8>(log)_2 6> log_3 6>(log)_4 6 (log)_2 8<(log)_4 6

Evaluate each of the following without using tables : (i) log 5 + log 8 - 2 log 2 (ii) log_(10) 8 + log_(10) 25 + 2 log_(10)3 - log_(10) 18 (iii) log 4 + (1)/(3) log 125 - (1)/(5) log 32

Solve for x, y , z . log_2 x + log_4 y + log_4 z =2 log_3 y + log_9 z + log_9 x =2 log_4 z + log_16 x + log_16 y =2

Solve (log_(3)x)(log_(5)9)- log_x 25 + log_(3) 2 = log_(3) 54 .

If 3^x=4^(x-1) , then x= (2(log)_3 2)/(2(log)_3 2-1) (b) 2/(2-(log)_2 3) 1/(1-(log)_4 3) (d) (2(log)_2 3)/(2(log)_2 3-1)

The value of log_(3) e- log_(9) e + log_(27) e- log_(81) e+…infty is