Prove that `log(a/b)+log(b/c)+log(c/a)=0`

Given a^2+b^2=c^2 . Prove that log_(b+c)a+log_(c-b)a=2 log_(c+b)a.log_(c-b)a,forallagt0,ane1 c-bgt0 , c+bgt0 c-bne1 , c+bne1 .

If a,b and c are in G.P., prove that log a, log b and log c are in A.P.

If a,b,c are distinct real number different from 1 such that (log_(b)a. log_(c)a-log_(a)a) + (log_(a)b.log_(c)b-log_(b)b) +(log_(a)c.log_(b)c-log_(c)C)=0 , then abc is equal to

Prove that : (1)/( log _(a) ^(abc) )+(1)/(log_(b)^(abc) ) + (1)/( log _c^(abc)) =1

Let agt0,cgt0,b=sqrtac,a,c and acne1,Ngt0 . Prove that log_aN/log_cN=(log_aN-log_bN)/(log_bN-log_cN)

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

Prove that: log_a x=log_bx xx log_c b xx…xx log_n m xx log_a n

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

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

The value of (bc)^log(b/c)*(ca)^log(c/a)*(ab)^log(a/b) is