Cho các số thực dương a;b;c thỏa mãn a^log3(7)

* Hướng dẫn giải

Chọn đáp án C 

Ta có: $c^{{\log }_{11}25}=121\iff c^{2{\log }_{11}5}={11}^2\Rightarrow c^{{\log }_{11}5}=11\Rightarrow 5^{{\log }_{11}c}=11$

Do đó

$P=a^{{\left({\log }_{3}7\right)}^2}+b^{{\left({\log }_{7}11\right)}^2}+5^{{\log }_{11}c}={\left(a^{{\log }_{3}7}\right)}^{{\log }_{3}7}+{\left(b^{{\log }_{7}11}\right)}^{{\log }_{7}11}+5^{{\log }_{11}c}$

$\begin{array}{l}=9^{{\log }_{3}7}+{49}^{{\log }_{7}11}+5^{{\log }_{11}c}\\ =3^{2{\log }_{3}7}+7^{2{\log }_{7}11}+5^{{\log }_{11}c}=3^{{\log }_3{7}^2}+7^{{\log }_7{11}^2}+5^{{\log }_{11}c}\\ =49+121+11=181\end{array}$