" 24."2(log a+log a^(2)+log a^(3)+log a^(4)+...)+log a^(n))" is equal to "

If a!=1 and ln a^(2)+(ln a^(2))^(2)+(ln a^(2))^(3)+...=3(ln a+(ln a)^(2)+(ln a)^(3)+(ln a)^(4)+......) then a is equal to

If a!=1 and In a^(2)+(In a^(2))^(2)+(In a^(2))3+...=3(ln a+(ln a)^(2)+(ln a)^(3)+(ln a)^(4)+...) then 'a' is equal to

Prove log a + log a^(2) + "log" a^(3) +……..+ log a^(n) = (n (n + 1))/(2) log a

[[log e, log e ^ (2), log e ^ (3) log e ^ (2), log e ^ (3), log e ^ (4) log e ^ (3), log e ^ (4) ), log e ^ (5)]]

If a_1,a_2,a_3,.....a_n.... are in G.P. then the determinant Delta=|[log a_n, log a_(n+1), log a_(n+2)],[log a_(n+3),loga_(n+4),log a_(n+5)],[log a_(n+6),log a_(n+7),log a_(n+8)]| is equal to- (A) -2 (B) 1 (C) -1 (D) 0

If y = log^nx , where log^n means log log log… (repeated n time), then x log x log^2 xlog^3 x…log^(n-1) xlog^n xdy/dx is equal to

If log ((a + b)/(2)) = (1)/(2) (log a + log b) , then a is equal to