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Câu hỏi: Cho $a$, $b$, $c$ là các số thực dương và $a\ne 1.$ Mệnh đề nào sau đây sai?
A. ${{\log }_{a}}\left( \dfrac{1}{b} \right)=-{{\log }_{a}}b$.
B. ${{\log }_{a}}\left( b+c \right)={{\log }_{a}}b.{{\log }_{a}}c$.
C. ${{\log }_{a}}\left( \dfrac{b}{c} \right)={{\log }_{a}}b-{{\log }_{a}}c$.
D. ${{\log }_{a}}\left( bc \right)={{\log }_{a}}b+{{\log }_{a}}c$.
A. ${{\log }_{a}}\left( \dfrac{1}{b} \right)=-{{\log }_{a}}b$.
B. ${{\log }_{a}}\left( b+c \right)={{\log }_{a}}b.{{\log }_{a}}c$.
C. ${{\log }_{a}}\left( \dfrac{b}{c} \right)={{\log }_{a}}b-{{\log }_{a}}c$.
D. ${{\log }_{a}}\left( bc \right)={{\log }_{a}}b+{{\log }_{a}}c$.
Áp dụng công thức về logrit ta thấy:
• ${{\log }_{a}}\left( \dfrac{1}{b} \right)={{\log }_{a}}{{\left( b \right)}^{-1}}=-{{\log }_{a}}b$.
• ${{\log }_{a}}\left( b+c \right)\ne {{\log }_{a}}b.{{\log }_{a}}c$.
• ${{\log }_{a}}\left( \dfrac{b}{c} \right)={{\log }_{a}}b-{{\log }_{a}}c$.
• ${{\log }_{a}}\left( bc \right)={{\log }_{a}}b+{{\log }_{a}}c$.
• ${{\log }_{a}}\left( \dfrac{1}{b} \right)={{\log }_{a}}{{\left( b \right)}^{-1}}=-{{\log }_{a}}b$.
• ${{\log }_{a}}\left( b+c \right)\ne {{\log }_{a}}b.{{\log }_{a}}c$.
• ${{\log }_{a}}\left( \dfrac{b}{c} \right)={{\log }_{a}}b-{{\log }_{a}}c$.
• ${{\log }_{a}}\left( bc \right)={{\log }_{a}}b+{{\log }_{a}}c$.
Đáp án B.
