If `a^(x-1)=b c , b^(y-1)=c a , c^(z-1)=a b` ,then `sum(1/x)=`

If a^(x-1)=bc,b^(y-1)=ca,c^(z-1)=ab, then sum((1)/(x))=

If a^(x)=b,b^(y)=c and c^(z)=a, prove that xyz=1

If a^(x)=b, b^(y)=c, c^(z)=a , then what is the value of (1)/((xy+yz+zx))((1)/(x)+(1)/(y)+(1)/(z)) ?

If a^x=b ,\ b^y=c\ a n d\ c^z=a , prove that x y z=1

If x=1+(log)_a b c , y=1+(log)_b c a and z=1+(log)_c a b , then prove that x y z=x y+y z+z x

Which of the foliowing statement(s) is/are true? (A) If a^x =b^y=c^z and a,b,c are in GP, then x, y, z are in HP (B) If a^(1/x)=b^(1/y)=c^(1/z) and a,b,c are in GP, then x,y,z are in AP