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Câu hỏi: Cho a là số thực dương và b là số thực khác 0. Mệnh đề nào sau đây là mệnh đề đúng?
A. ${{\log }_{3}}\left( \dfrac{3{{a}^{3}}}{{{b}^{2}}} \right)=1+\dfrac{1}{3}{{\log }_{3}}a-2{{\log }_{3}}\left| b \right|.$
B. ${{\log }_{3}}\left( \dfrac{3{{a}^{3}}}{{{b}^{2}}} \right)=1+3{{\log }_{3}}a-2{{\log }_{3}}b.$
C. ${{\log }_{3}}\left( \dfrac{3{{a}^{3}}}{{{b}^{2}}} \right)=1+3{{\log }_{3}}a+2{{\log }_{3}}b.$
D. ${{\log }_{3}}\left( \dfrac{3{{a}^{3}}}{{{b}^{2}}} \right)=1+3{{\log }_{3}}a-2{{\log }_{3}}\left| b \right|.$
A. ${{\log }_{3}}\left( \dfrac{3{{a}^{3}}}{{{b}^{2}}} \right)=1+\dfrac{1}{3}{{\log }_{3}}a-2{{\log }_{3}}\left| b \right|.$
B. ${{\log }_{3}}\left( \dfrac{3{{a}^{3}}}{{{b}^{2}}} \right)=1+3{{\log }_{3}}a-2{{\log }_{3}}b.$
C. ${{\log }_{3}}\left( \dfrac{3{{a}^{3}}}{{{b}^{2}}} \right)=1+3{{\log }_{3}}a+2{{\log }_{3}}b.$
D. ${{\log }_{3}}\left( \dfrac{3{{a}^{3}}}{{{b}^{2}}} \right)=1+3{{\log }_{3}}a-2{{\log }_{3}}\left| b \right|.$
Vì $a>0,b\ne 0$
Ta có ${{\log }_{3}}\left( \dfrac{3{{a}^{3}}}{{{b}^{2}}} \right)={{\log }_{3}}3{{a}^{3}}-{{\log }_{3}}{{b}^{2}}={{\log }_{3}}3+{{\log }_{3}}{{a}^{3}}-{{\log }_{3}}{{b}^{2}}=1+3{{\log }_{3}}a-2{{\log }_{3}}\left| b \right|$
Ta có ${{\log }_{3}}\left( \dfrac{3{{a}^{3}}}{{{b}^{2}}} \right)={{\log }_{3}}3{{a}^{3}}-{{\log }_{3}}{{b}^{2}}={{\log }_{3}}3+{{\log }_{3}}{{a}^{3}}-{{\log }_{3}}{{b}^{2}}=1+3{{\log }_{3}}a-2{{\log }_{3}}\left| b \right|$
Đáp án D.