Question 4
Let $x,$ $y,$ and $z$ be positive real numbers that satisfy the following system of equations: $$
\log_2\left(\frac{x}{yz}\right) = \frac{1}{2}
$$ $$
\log_2\left(\frac{y}{xz}\right) = \frac{1}{3}
$$ $$
\log_2\left(\frac{z}{xy}\right) = \frac{1}{4}
$$
Then the value of $\left|\log_2(x^4 y^3 z^2)\right|$ is $\frac{m}{n}$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$
\log_2\left(\frac{x}{yz}\right) = \frac{1}{2}
$$ $$
\log_2\left(\frac{y}{xz}\right) = \frac{1}{3}
$$ $$
\log_2\left(\frac{z}{xy}\right) = \frac{1}{4}
$$
Then the value of $\left|\log_2(x^4 y^3 z^2)\right|$ is $\frac{m}{n}$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$