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* Hướng dẫn giải

\(\begin{array}{l} {\log _{{a^2}}}\left( {{a^{10}}{b^2}} \right) + {\log _{\sqrt a }}\left( {\frac{a}{{\sqrt b }}} \right) + {\log _{\sqrt[3]{b}}}\left( {{b^{ - 2}}} \right)\\ = {\log _{{a^2}}}{a^{10}} + {\log _{{a^2}}}{b^2} + {\log _{\sqrt a }}a - {\log _{\sqrt a }}\sqrt b + {\log _{{b^{\frac{1}{3}}}}}\left( {{b^{ - 2}}} \right)\\ = \frac{{10}}{2}{\log _a}a + \frac{2}{2}{\log _a}b + {\log _{{a^{\frac{1}{2}}}}}a - {\log _{{a^{\frac{1}{2}}}}}{b^{\frac{1}{2}}} + \frac{{ - 2}}{{\frac{1}{3}}}{\log _b}b\\ = 5 + {\log _a}b + 2 - {\log _a}b - 6=1 \end{array}\)