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Câu hỏi: Giá trị của biểu thức $P=3^{1+\log _{9} 4}+4^{2-\log _{2} 3}+5^{\log _{125} 27}$ là?
A. $P=\dfrac{99}{8}$.
B. $P=\dfrac{97}{8}$.
C. $P=\dfrac{98}{9}$.
D. $P=\dfrac{97}{9}$.
A. $P=\dfrac{99}{8}$.
B. $P=\dfrac{97}{8}$.
C. $P=\dfrac{98}{9}$.
D. $P=\dfrac{97}{9}$.
Ta có $P={{3.3}^{{{\log }_{{{3}^{2}}}}{{2}^{2}}}}+\dfrac{16}{{{4}^{{{\log }_{2}}3}}}+{{5}^{{{\log }_{{{5}^{3}}}}{{3}^{3}}}}$
$=3.3^{\log _{3} 2}+\dfrac{16}{3^{\log _{2} 4}}+5^{\log _{5} 3}=3.2^{\log _{3} 3}+\dfrac{16}{3^{2 \log _{2} 2}}+3^{\log _{5} 5}=3.2+\dfrac{16}{3^{2}}+3=\dfrac{97}{9}$.
$=3.3^{\log _{3} 2}+\dfrac{16}{3^{\log _{2} 4}}+5^{\log _{5} 3}=3.2^{\log _{3} 3}+\dfrac{16}{3^{2 \log _{2} 2}}+3^{\log _{5} 5}=3.2+\dfrac{16}{3^{2}}+3=\dfrac{97}{9}$.
Đáp án D.