If `(loga)/(b-c)=(logb)/(c-a)=(logc)/(a-b)`, then prove that `(a^a)(b^b)(c^c)=1`.

if loga/(b-c)=logb/(c-a)=logc/(a-b) then find the value of a^ab^bc^c

If loga/(b-c) = logb/(c-a) = logc/(a-b) , then a^(b+c).b^(c+a).c^(a+b) =

If loga/(b-c) = logb/(c-a) = logc/(a-b) , then a^(b+c).b^(c+a).c^(a+b) =

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

If (a(b+c-a))/(loga) = (b(c+a-b))/(logb) = (c(a+b-c))/(logc) , then prove that b^(c ) . c^(b) = a^(c ).c^(a) = a^(b).b^(a) .

If a, b, c are distinct positive real numbers each different from unity such that (log_b a.log_c a -log_a a) + (log_a b.log_c b-logb_ b) + (log_a c.log_b c - log_c c) = 0, then prove that abc = 1.

if x =log_a (bc), y= log_b (ca) and z=log_c(ab) then 1/(x+1)+1/(y+1)+1/(z+1)

If log((a+b)/(6))=(1)/(2)(loga+logb) , then (a)/(b) + (b)/(a) = ______.