Prove that :
(i) `log(1^(1/5)+32^(1/5)+243^(1/5))=1/5(log1 + log 32 + log 243)`.

Prove that log_(2) [log_(4) {log_(5) (625)^(4)}]=1

Prove that: log_(3)log_(2)log_(sqrt(5))(625)=1

Prove that log(75/16)-2log(5/9)+log(32/243)=log2

Prove that: log_3log_2log_(sqrt(5))(625)=1

(1)/(2)log_(5)36+2log_(5)7-(1)/(2)log_(5)12

Prove that log frac(75)(16)-2log frac(5)(9)+log frac(32)(243)=log2

Express in terms of log 2 and log 3 : (i) log 36 (ii) log 144 (iii) log 4.5 (iv) "log"(26)/(51) - "log" (91)/(119) (v) "log"(75)/(16) - "2 log" (5)/(9) + "log" (32)/(243)

Prove that : log_e(n+1)-log_e(n-1)=2[1/n+1/(3n^3)+1/(5n^5)+...]

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