Prove that `log_2log_2log_(2) 16 =1`

Prove that log_3log_2log_(sqrt3) 81=1

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

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

Prove that: (log_a(log_ba))/(log_b(log_ab))=-log_ab

If log_(a) 3 = 2 and log_(b) 8 = 3," then prove that "log_(a) b= log_(3) 4 .

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

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

(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(1+2+3)=log1+log2+log3

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