The great log (part 2)

Algebra Level 3

\[\large 5^{\log_{1/5} \left(\frac12 \right)} + \log_{\sqrt2} \left( \dfrac4{\sqrt7+\sqrt3} \right) + \log_{1/2} \left ( \dfrac1{10+2\sqrt{21}} \right) = \, ? \]

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