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

a^(x)=b^(y)=c^(z) and b^(2)=ac then prove that (1)/(x)+(1)/(z)=(2)/(y)

a(y+z)=x,b(z+x)=y,c(x+y)=z prove that (x^(2))/(a(1-bc))=(y^(2))/(b(1-ca))=(z^(2))/(c(1-ab))

If |(a,y,z),(x,b,z),(x,y,c)|=0 , then prove that (a)/(a-x)+(b)/(b-y)+(c)/(c-z)=2

The value of the determinant ,log_(a)((x)/(y)),log_(a)((y)/(z)),log_(a)((z)/(x))log_(b)((y)/(z)),log_(b)((z)/(x)),log_(b)((x)/(y))log_(c)((z)/(x)),log_(c)((x)/(y)),log_(c)((y)/(z))]|

If a(y+z)=b(z+x)=c(x+y) then show that (a-b)/(x^(2)-y^(2))=(b-c)/(y^(2)-z^(2))=(c-a)/(z^(2)-x^(2))]

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)) ?

The value of ((x-y)^(3)+(y-z)^(3)+(z-x)^(3))/(9(x-y)(y-z)(z-x)) is equal to (a)0(b)(1)/(9)(c)(1)/(3)(d)1

if a,b,c are in G.P. and a^(x)=b^(y)=c^(z) prove that (1)/(x)+(1)/(z)=(2)/(y)

If x=(a-b)/(a+b), y=(b-c)/(b+c) and z=(c-a)/(c+a) , find the value of ((1+x)(1+y)(1+z))/((1-x)(1-y)(1-z))