Question

The expression `((log_(a/b) p)^2+(log_(b/c) p)^2+(log_(c/a) p)^2)/((log_(a/b) p+log_(b/c) p+log_(c/a) p))^2,` wherever defined, simplifies to
A. 1
B. 2
C. 3
D. 4

Answer 1

`T_(1)=(log_(a/b)P)^(2)=(1)/((log_(p)""(a)/(b))^(2))=(1)/((log_(p)a-(log_(p)b))^(2)),log=x,log_(p)b=y andlog_(p)c=z`
`impliesT_(1)=(1)/((x-y)^(2))," "T_(2)=(1)/((y-z)^(2))andT_(3)=(1)/((z-y)^(2))`
`Hence E=((1)/((x-y)^(2))+(1)/((y-z)^(2))+(1)/((z-y)^(2)))/((1/(x-y)+1/(y-z)+1/(z-x)))=1`