Question

if x square+y square=25xy then prove that 2 log (x+y) = 3log3 + log x + log y



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Answer 1

Answer :

Now,

x² + y² = 25xy

⇒ (x + y)² - 2xy = 25xy

⇒ (x + y)² = 25xy + 2xy

⇒ (x + y)² = 27xy

Now, taking (log) to both sides, we get

log (x + y)² = log (27xy)

⇒ 2 log(x + y) = log (27) + logx + logy

[ since log (a^b) = b loga
and log (abc) = loga + logb + logc ]

⇒ 2 log(x + y) = log (3³) + logx + logy

⇒ 2 log(x + y) = 3 log3 + logx + logy

[ since log (a^b) = b loga ]

[ Proved ]

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