Sometimes logs logs our mind too!

Algebra Level 3

\[ \begin{eqnarray} a & = & \frac { \log_{27} 8}{\log_ 3 2} \\ b & = & \left ( \frac 1 {2^{\log_2 5}} \right ) \left ( \frac 1 {5^{\log_5 0.1}}\right ) \\ c & = & 2^{\sqrt{\log_2 5}} - 5^{\sqrt{\log_5 2}} \\ \end{eqnarray} \]

What is the value of \(a+b+c\)?

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