`log (a+b) + log(a-b) - log(a^2-b^2)=`

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.

Prove the following identities: (a) (log_(a) n)/(log_(ab) n) = 1+ log_(a) b" "(b) log_(ab) x = (log_(a) x log_(b) x)/(log_(a) x + log_(b) x) .

Statement-1: The solution set of the equation "log"_(x) 2 xx "log"_(2x) 2 = "log"_(4x) 2 "is" {2^(-sqrt(2)), 2^(sqrt(2))}. Statement-2 : "log"_(b)a = (1)/("log"_(a)b) " and log"_(a) xy = "log"_(a) x + "log"_(a)y

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

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

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 :

If the left hand side of the equation a(b-c)x^2+b(c-a) xy+c(a-b)y^2=0 is a perfect square , the value of {(log(a+c)+log(a-2b+c)^2)/log(a-c)}^2 , (a,b,cinR^+,agtc) is

Let (log a)/( b-c) = (logb)/(c-a) = (log c)/(a-b) STATEMENT 1: a^(a) b^(b) c^(c) = 1 STATEMENT 2: a^(b+c) b^(c +a) c^(a + b) = 1