If x²+y²=11 x y, then 2 (x-y)=

Correct Answer is : 2log⁡3+log⁡x+log⁡y2 3+ x+ y2log3+logx+logy

Correct Answer is : 2log⁡3+log⁡x+log⁡y2 3+ x+ y2log3+logx+logy

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Logarithms

Question : 27 of 85

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x^{2}+y^{2}=11 x y,

2 \log (x-y)=

Solution:

Concept:

Manipulate the given equation to express

(x-y)^2

in terms of

xy

Explanation:

Given

x^{2}+y^{2}=11xy

Rewrite:

x^{2} - 2xy + y^{2} = 9xy

Thus

(x-y)^2 = 9xy

Taking square root (assuming

x>y>0

for positive arguments):

x-y = 3\sqrt{xy}

Take common log:

\log(x-y) = \log 3 + \log\sqrt{xy} = \log 3 + \frac{1}{2}(\log x + \log y)

Multiply by 2:

2\log(x-y) = 2\log 3 + \log x + \log y

Answer:

Option C:

2\log 3 + \log x + \log y

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