Cho $\Large \log_{3}5=a, \log_{3}6=b, \log_{3}22=c$. Mệnh đề nào sau đ

Cho $\Large \log_{3}5=a, \log_{3}6=b, \log_{3}22=c$. Mệnh đề nào sau đây là đúng?

• A.

  A. $\Large \log_{3}\left(\dfrac{270}{121}\right)=a+3b-2c$

   
• B.

  B. $\Large \log_{3}\left(\dfrac{270}{121}\right)=a+3b+2c$

• C.

  C. $\Large \log_{3}\left(\dfrac{270}{121}\right)=a-3b+2c$

• D.

  D. $\Large \log_{3}\left(\dfrac{270}{121}\right)=a-3b-2c$

Chọn A

$\Large \log_{3}6=b \Leftrightarrow \log_{3}(3.2)=b \Leftrightarrow 1+\log_{3}2=b\Leftrightarrow \log_{3}2=b-1\\\Large \log_{3}22=c\Leftrightarrow \log_{3}(11.2)=c\Leftrightarrow \log_{3}11+\log_{3}2=c\\\Large \Leftrightarrow \log_{3}11=c-\log_{3}2=c-b+1\\\Large \log_{3}\left(\dfrac{270}{121}\right)=\log_{3}\left(\dfrac{2.3^3.5}{11^2}\right)=\log_{3}(2.3^3.5)-2\log_{3}11\\\Large =\log_{3}2+3+\log_{3}5-2\log_{3}11=b-1+3+a-2(c-b+1)=a+3b-2c$