Question

if x²+y²=25xythen prove that 2log (x+y)=3log+log x +log y









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Answer 1

Answer:

Given:-

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• x^2 +y^2 =25xy

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$\sf \: \longrightarrow x^{2} + y^{2} + 2xy = 25xy + 2xy$

$\sf \: \longrightarrow (x+ y)^{2} = 27xy$

$\sf \: \longrightarrow (x+ y)^{2} = 3^{3}xy$

$\sf \: \longrightarrow log (x+y)^{2} = log ( 3^{3}xy )$

$\sf \: \longrightarrow 2 \: \: log (x+y) = log \: 3^{3} + log \: x + log \: y$

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*/ By Logarithmic laws /*

• 1. log aⁿ = n log a

• 2. log mn = log m + log n

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$\sf \: \longrightarrow2 \: log \: (x+y) =3 \: log \: 3+ log \: x + log \: \: y$

Answer 2

Step-by-step explanation:

topic :

• log

given :

• if x²+y²=25xy
• prove that 2log (x+y)=3log+log x +log y

to find :

• 2log (x+y)=3log+log x +log y = ?

• 2log (x+y)=3log+log x +log y = ?

solution :

• x² + y² = 25xy

• L.H.S= 2log(x + y)

• = log(x + y)²

• = log(x² + y² + 2xy) -

• = log (25xy + 2xy) [from (1)]

then, we will substitute them

• = log(27xy)

• = log (3³ xy)

• = log3³+ logx + logy

• = 3log3+ logx + logy