Question

If $\log \left(\frac{x+y}{5}\right)=\frac{1}{2}(\log x+\log y)$, then $\frac{x}{y}+\frac{y}{x}=$

• A. $5$
• B. $10$
• C. $23$
• D. $1$

Answer 1

The correct option is C $23$

We have,

$log\left(\frac{x+y}{5}\right)=\frac{1}{2}(logx+logy)$

$log\left(\frac{x+y}{5}\right)=\frac{1}{2}\left(logxy\right)$

$log\left(\frac{x+y}{5}\right)=log\sqrt{xy}$

$\frac{x+y}{5}=\sqrt{xy}$

$\frac{x^2+y^2+2xy}{25}=xy$

$x^2+y^2+2xy=25xy$

$x^2+y^2=23xy$

$\frac{x^2}{xy}+\frac{y^2}{xy}=23$

$\frac{x}{y}+\frac{y}{x}=23$

Hence, this is the answer.