If `a,b,c` are positive reral numbers such that `(loga)/(b-c)=(logb)/(c-a)=(logc)/(a-b),`then prove that

If a,b,c are positive reral numbers such that (log a)/(b-c)=(log b)/(c-a)=(log c)/(a-b), then prove that

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 a, b, c are positive real numbers, then the minimum value of a^(logb-logc)+b^(logc-loga)+c^(loga-logb) is

If a, b, c are positive real numbers, then the minimum value of a^(logb-logc)+b^(logc-loga)+c^(loga-logb) is

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) =

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 is a positive real number different from 1 such that log_a x, log_b x, log_c x are in A.P then