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

log_(2)4+ log_(4)4 + log_(16)4 is equal to

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

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

[[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 log a+log (a^(2)/b)+log (a^(3)/b^(2))+.. .. n terms =(n)/(2)(P log a+Q log b) then P Q=

If x=3, then log_(4)(2log_(3)(1+log_(2)(1+3log_(3)x))) is equal to