Logarithmic Tactics!

$\large \log x + \dfrac{ \log(xy^8)}{(\log x)^2 + (\log y)^2 } = 2, \qquad \log y + \dfrac{ \log \left( \dfrac{x^8}y \right)}{(\log x)^2 + (\log y)^2 } = 0$

Let $x$ and $y$ satisfy the system of equations above. Find the product $xy$ .

#Algebra

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Is ithe dot multiplication sign or subtraction?

If multiplication , then take ligx=a and logy=b and then proceed.It would be easier now.

Harsh Shrivastava - 5 years, 1 month ago

Its Logx+log(xy^8)/(logx)²+(logy)²=2

Logy+log(x^8y)/(logx)²+(logy)²=0

naitik sanghavi - 5 years, 1 month ago

Where is the answer

Eternal Dragon - 3 years, 10 months ago

@Pi Han Goh ,Thanks!

Can you help me solve this!?

naitik sanghavi - 5 years, 1 month ago

@Calvin Lin @Nihar Mahajan @Swapnil Das @Svatejas Shivakumar @Sravanth Chebrolu @Brian Charlesworth @Rajdeep Dhingra @Mehul Arora can someone help me!

naitik sanghavi - 5 years, 1 month ago

Please limit your @mentions to at most 5 people.

Abdur Rehman Zahid - 5 years, 1 month ago

Sorry for that,but still no one replied !!

naitik sanghavi - 5 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$