`log_(e^(2))^(a^(b))*log_(a^(3))^(b^(c))log_(b^(4))^(e^(a))`

The sum of the series log_(a)b+log_(a^(2))b^(2)+log_(a^(3))b^(3)+....log_(a^(n))b^(n)

The value of log_(b)a+log_(b^(2))a^(2) + log_(b^(3))a^(3) + ... + log_(b^(n))a^(n)

The value of (6 a^(log_(e)b)(log_(a^(2))b)(log_(b^(2))a))/(e^(log_(e)a*log_(e)b)) is

Suppose 1 lt a lt sqrt(e) and log_(e)a^(2)+(log_(e)a^(2))^(2)+(log_(e)a^(2))^(3)+…. =3 [log_(e)a+(log_(e)a)^(2)+(log_(e)a)^(3)+…]" (1)" then log_(e)(a^(3))=

a^(log_(b)c)=c^(log_(b)a)

The minimum value of 'c' such that log_(b)(a^(log_(2)b))=log_(a)(b^(log_(2)b)) and log_(a) (c-(b-a)^(2))=3 , where a, b in N is :

The expression ((log_((a)/(b))p)^(2)+(log_((b)/(c))p)^(2)+(log_((a)/(a))p)^(2))/(((log_((a)/(b))p+log_((b)/(c))p+log_((c)/(a))p))^(2)) wherever defined,simplifies to

log (a^(2)/b)+log(a^(4)/b^(3)) + log (a^(6)/b^(3))+…… +log ((a^(2n))/b^(n))=?