MathDB

Let

x,y

and

z

be positive real numbers that satisfy the following system of equations:

\log_2\left({x \over yz}\right) = {1 \over 2}

\log_2\left({y \over xz}\right) = {1 \over 3}

\log_2\left({z \over xy}\right) = {1 \over 4}

Then the value of

\left|\log_2(x^4y^3z^2)\right|

{m \over n}

where

m

and

n

are relatively prime positive integers. Find

m+n

Problem Statement