Cho các số thực $a,b,c$ thỏa mãn ${{a}^{{{\log }_{3}}7}}=27,{{b}^{{{\log }_{7}}11}}=49,{{c}^{{{\log }_{11}}25}}=\sqrt{11}.$ Giá trị của biểu thức...

Ta có $A={{a}^{{{\left( {{\log }_{3}}7 \right)}^{2}}}}+{{b}^{{{\left( {{\log }_{7}}11 \right)}^{2}}}}+{{c}^{{{\left( {{\log }_{11}}25 \right)}_{2}}}}={{\left( {{a}^{{{\log }_{3}}7}} \right)}^{{{\log }_{3}}7}}+{{\left( {{b}^{{{\log }_{7}}11}} \right)}^{{{\log }_{7}}11}}+{{\left( {{c}^{{{\log }_{11}}25}} \right)}^{{{\log }_{11}}25}}$
$={{27}^{{{\log }_{3}}7}}+{{49}^{{{\log }_{7}}11}}+{{\sqrt{11}}^{{{\log }_{11}}25}}={{\left( {{3}^{{{\log }_{3}}7}} \right)}^{3}}+{{\left( {{7}^{{{\log }_{7}}11}} \right)}^{2}}+{{\left( {{11}^{{{\log }_{11}}25}} \right)}^{\dfrac{1}{2}}}={{7}^{3}}+{{11}^{2}}+{{25}^{\dfrac{1}{2}}}=469.$