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Câu hỏi: Rút gọn biểu thức $P={{3}^{2{{\log }_{3}}a}}-{{\log }_{5}}{{a}^{2}}.{{\log }_{a}}25$
A. ${{a}^{2}}-2$
B. ${{a}^{2}}+4$
C. ${{a}^{2}}-4$
D. ${{a}^{2}}+2$
A. ${{a}^{2}}-2$
B. ${{a}^{2}}+4$
C. ${{a}^{2}}-4$
D. ${{a}^{2}}+2$
Điều kiện: $\left\{ \begin{aligned}
& a>0 \\
& a\ne 1 \\
\end{aligned} \right.$.
Ta có: $P={{3}^{2{{\log }_{3}}a}}-{{\log }_{5}}{{a}^{2}}.{{\log }_{a}}25={{\left( {{3}^{{{\log }_{3}}a}} \right)}^{2}}-2\left( {{\log }_{5}}a \right).\left( 2{{\log }_{a}}5 \right)$
$={{a}^{2}}-4{{\log }_{5}}a.{{\log }_{a}}5={{a}^{2}}-4$
& a>0 \\
& a\ne 1 \\
\end{aligned} \right.$.
Ta có: $P={{3}^{2{{\log }_{3}}a}}-{{\log }_{5}}{{a}^{2}}.{{\log }_{a}}25={{\left( {{3}^{{{\log }_{3}}a}} \right)}^{2}}-2\left( {{\log }_{5}}a \right).\left( 2{{\log }_{a}}5 \right)$
$={{a}^{2}}-4{{\log }_{5}}a.{{\log }_{a}}5={{a}^{2}}-4$
Đáp án C.