If x and y and are positive numbers connected by the relation y = ax²/(x-a) (x-b) (x-c) + bx/(x-b) (x-c) + c / (x-c) + 1 then prove that log y = 3log x-log | x-a|- log | x-b|- log | x-c|for any valid base of logarithms.

Daer ajit

simplify the equation

y = ax²+ bx(x-a)+c(x-a)(x-c)/(x-a)(x-b)x-c) +1

ax²+ bx(x-a)+c(x-a)(x-c =x³- (x-a)(x-b)(x-c)+1

y=x³/(x-a)(x-b)(x-c) -1+1

so

log(y) = 3log x-log | x-a|- log | x-b|- log | x-c|

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