${\log ^{35}} + 2{\log ^{2\sqrt 7 }} - {\log ^{200}} - 2{\log ^7} = $${\log ^{35}} + {\log ^{{{\left( {2\sqrt 7 } \right)}^2}}} - {\log ^{200}} - {\log ^{{7^2}}} = $${\log ^{\frac{{35 \times 4 \times 7}}{{200 \times {7^2}}}}} = {\log ^{\frac{1}{{10}}}} = \log _{10}^{{{10}^{ - 1}}} =  - 1$