prove that `log2 + 16 log(16/15) + 12 log(25/24) + 7 log(81/80) = 1 `

Find the value of 7 log(16/15) + 5 log (25/24) + 3 log (81/80) .

Prove that log_2log_2log_(2) 16 =1

Prove that : "2 log" (15)/(18) - "log" (25)/(162) + "log" (4)/(9) = log 2

Prove that log_3log_2log_(sqrt3) 81=1

Prove that : (log_(2)10)(log_(2)80)-(log_(2)5)(log_(2)160)=4 .

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

If 0ltxlt1 , prove that: log(1+x)+log(1+x^2)+log(1+x^4)+… oo=-log(1-x)

(i) Show that (log 9)/2 + 2 log 6 +(log 81)/4 - log 12 = 3 log 3 .

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

Evaluate : (i) log_(125) 625 - log_(16) 64 (ii) log_(16) 32 - log_(25) 125 + log_(9) 27 .