<p>There exist real numbers <img alt="$x$" height="10" src="https://latex.artofproblemsolving.com/2/6/e/26eeb5258ca5099acf8fe96b2a1049c48c89a5e6.png" width="12" /> and <img alt="$y$" height="13" src="https://latex.artofproblemsolving.com/0/9/2/092e364e1d9d19ad5fffb0b46ef4cc7f2da02c1c.png" width="11" />, both greater than 1, such that <img alt="$\log_x\left(y^x\right)=\log_y\left(x^{4y}\right)=10$" height="24" src="https://latex.artofproblemsolving.com/b/0/0/b00ba57d66f11bcd019e0474ebfeb18a570919f8.png" width="211" />. Find <img alt="$xy$" height="11" src="https://latex.artofproblemsolving.com/3/f/7/3f79c3676b62fb47243e0d357c87115b6f3395e4.png" width="19" />.</p>

Question No: 418

There exist real numbers $x$ and $y$ , both greater than 1, such that $\log_x\left(y^x\right)=\log_y\left(x^{4y}\right)=10$ . Find $xy$ .

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Tags: Algebra

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