# Logarithms!

Algebra Level 4

\large \begin{aligned} \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{aligned}

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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