# Lost Logarithm III

Algebra Level 1

$\large \color{green}x \color{brown}y=10^a, \quad \color{brown}y \color{red}z=10^b, \quad \color{green}x \color{red}z=10^c$

Consider the system of equations above, what is $$\log \ \color{green} x +\log \ \color{brown}y+ \log \ \color{red}z$$?

Details and Assumptions:

The logarithms have base of $$10$$

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