Logarithm

1) If

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

Then prove that

$$ x^2+y^2=6xy$$

2)if

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

Than prove that

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

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