if x square+y square=25xy then prove that 2 log (x+y) = 3log3 + log x + log y
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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 ]
#MarkAsBrainliest
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 ]
#MarkAsBrainliest
sanjay354:
Thanks
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