Show that the sequence `loga ,log((a^2)/b),log((a^3)/(b^2)),log((a^4)/(b^3)), ` forms an A.P.

Show that the sequence loga ,log(a b),log(a b^2),log(a b^3), is an A.P. Find the nth term.

Show that the sequence loga ,log(a b),log(a b^2),log(a b^3), is an A.P. Find its nth term.

Show that the sequence loga ,log(a b),log(a b^2),log(a b^3), is an A.P. Find its nth term.

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 value of ("log"_(a)("log"_(b)a))/("log"_(b)("log"_(a)b)) , is

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

Prove that : (i) (log a)^(2) - (log b)^(2) = log((a)/(b)).log(ab) (ii) If a log b + b log a - 1 = 0, then b^(a).a^(b) = 10

If log_(a)b+log_(b)c+log_(c)a vanishes where a, b and c are positive reals different than unity then the value of (log_(a)b)^(3) + (log_(b)c)^(3) + (log_(c)a)^(3) is

If log( (2 b)/(3c)), log((4c)/(9a)) and log((8a)/(27b)) are in A.P. where a,b,c and are in G.P. then a,b,c are the length of sides of (A) a scelene triangle (B) anisocsceles tirangel (C) an equilateral triangle (D) none of these

Prove that asqrt(log_a b)-bsqrt(log_b a)=0