PART 8：例題-連鎖定理

\(\left( {{\log }_{3}}7 \right)\left( {{\log }_{7}}8 \right)\left( {{\log }_{8}}27 \right)=?\)

SOL:

\(\left( {{\log }_{9}}7 \right)\left( {{\log }_{7}}8 \right)\left( {{\log }_{8}}27 \right)\) \(=\frac{{{\log }_{3}}7}{{{\log }_{3}}9}\cdot \frac{{{\log }_{3}}8}{{{\log }_{3}}7}\cdot \frac{{{\log }_{3}}27}{{{\log }_{3}}8}=\frac{{{\log }_{3}}27}{{{\log }_{3}}9}=\frac{3}{2}\)