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

If (log a)/(b-c)=(log b)/(c-a)=(log c)/(a-b), then prove that (a^(a))(b^(c))(c^(c))=1

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

If (log x)/(b-c) = (log y)/(c-a) = (log z)/(a-b) , then prove that x^(b+c).y^(c+a).z^(a+b) = 1

a,b,c are positive real numbers such that log a(b-c)=(log b)/(c-a)=(log c)/(a-b) then prove that (1)a^(b+c)+b^(c+a)+c(a+b)>=3(2)a^(a)+b^(b)+c^(c)>=3

If (log a)/(b-c)=(log b)/(c-a)=(log c)/(a-b) then a^(a)*b^(b)*c^(c)=

If (log a)/(b-c)=(log b)/(c-a)=(log c)/(a-b), then a^(b+c)+b^(c+a)+c^(a+b) is

If (log a)/(b-c)=(log b)/(c-a)=(log c)/(a-b), then a^(b+c)*b^(c+a)*c^(a+b)=

if (log a)/(b-c)=(log b)/(c-a)=(log c)/(a-b) then find the value of a^(a)b^(b)c^(c)