If \;x+y/7=\;1/2( x+ y) then,

Correct Answer is : xy+ yx=47\;x/y+\;y/x=47yx+xy=47

Correct Answer is : xy+ yx=47\;x/y+\;y/x=47yx+xy=47

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Logarithms

Question : 37 of 85

Marks: +1, -0

\log\;\frac{x+y}{7}=\;\frac{1}{2}(\log x+\log y)

then,

Solution:

Concept:

Use logarithm properties to simplify and then derive the required expression.

Explanation:

Given:

\log \frac{x+y}{7} = \frac{1}{2}(\log x + \log y)

By logarithm addition,

\log x + \log y = \log(xy)

So RHS becomes

\frac{1}{2} \log(xy) = \log \sqrt{xy}

Thus

\log \frac{x+y}{7} = \log \sqrt{xy}

Since

\log

is one-to-one,

\frac{x+y}{7} = \sqrt{xy}

Multiply by 7:

x+y = 7\sqrt{xy}

Square both sides:

(x+y)^2 = 49xy

Expand:

x^2 + 2xy + y^2 = 49xy

, so

x^2 + y^2 = 47xy

Divide by

xy

\frac{x^2}{xy} + \frac{y^2}{xy} = 47

, i.e.,

\frac{x}{y} + \frac{y}{x} = 47

Answer:

\frac{x}{y} + \frac{y}{x} = 47

, which corresponds to option C.

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