If x^4 + y^4 = 83x^2y^2 then prove that log (x^2/9-y^2/9) = log x + logy

Question

Mathematics

Sydnee Berger

20 June, 18:37

If x^4 + y^4 = 83x^2y^2 then prove that log (x^2/9-y^2/9) = log x + logy

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Tyrell Barron · Answer 1

x^4 + y^4 = 83x^2y^2

x^4+y^4-2x^2y^2 = 83x^2y^2

x^4-2x^2y^2+y^4 = 81x^2y^2

(x^2-y^2) ^2 = 81x^2y^2

x^2-y^2 = 9xy

log (x^2-y^2) = log (xy)

log (x^2-y^2) = log 9 + logxy

log (x^2-y^2) - log 9 = logxy

log (x^2/9-y^2/9) = logy