# Logarithms!

Algebra Level 4

$\large \begin{eqnarray} \log_2 x + \log_4 y + \log_4 z &=& 2 \\ \log_3 y + \log_9 z + \log_9 x &=& 2 \\ \log_4 z + \log_{16} x + \log_{16} y &=& 2 \end{eqnarray}$

Solve the system equations where $$x$$ , $$y$$ and $$z$$ are positive real numbers.

If the value $$x,y,z$$ can be written in the form $$\dfrac{a_x}{b_x} , \dfrac{a_y}{b_y} , \dfrac{a_z}{b_z}$$ for co-prime $$a_i , a_j$$, find the value of $$a_x+b_x+a_y+b_y+a_z+b_z$$.

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