Sometimes logs logs our mind too!

Algebra Level 3

a=log278log32b=(12log25)(15log50.1)c=2log255log52 \begin{aligned} 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{aligned}

What is the value of a+b+ca+b+c?

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