Prove that `log(1+2+3)=log1+log2+log3`

Prove that: 2log(1+2+4+7+14)= log1+log2+log4+log7+log14

Prove that log_2log_2log_(2) 16 =1

(i) If log(a + 1) = log(4a - 3) - log 3, find a. (ii) If 2 log y - log x - 3 = 0, express x in termss of y. (iii) Prove that : log_(10) 125 = 3(1 - log_(10)2) .

Prove that: log sin 8x = 3 log2+log sin x+ log cos 2x+log cos 4x

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

Prove that log_3log_2log_(sqrt3) 81=1

If a^(2) + b^(2) = 7 ab," prove that " log((a+b)/3) = 1/2 (log a + log b) .

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

Prove that: (log_9 11)/(log_5 3) = (log_3 11)/(log_sqrt(5) 3).

Prove that (log_(2)8)/(log_(3)9) =3/2