Cho log (12) 18= a + b/(c+log (2) 3) .Tính tông a+b+c

$log_{12}18=\dfrac{log_218}{log_212}=\dfrac{log_2(2.3^2)}{log2(2^2.3)}=\dfrac{1+2log_23}{2+log_23}=\dfrac{4+2log_23-3}{2+log_23}=2+\dfrac{-3}{2+log_23}\\=a+\dfrac{b}{c+log_23}=>a+b+c=2+2-3=1$

`log_{12} 18 = a + b/(c + log_{2} 3)`

`text{Ta có}`

`log_{12} 18`

`= (log_{2} 18)/(log_{2} 12)`

`= (log_{2} (2.3^{2)))/(log_{2} (3.2^{2}))`

`= (log_{2} 2 + 2log_{2} 3)/(log_{2} 2^{2} + log_{2} 3)`

`= (1 + 2log_{2} 3)/(2 + log_{2} 3)`

`= (4 + 2log_{2} 3 - 3)/(2 + log_{2} 3)`

`= (2(2 + log_{2} 3))/(2 + log_{2} 3) + (-3)/(2 + log_{2} 3)`

`= 2 + (-3)/(2 + log_{2} 3) = a + b/(c + log_{2} 3)`

`->` \(\left\{ \begin{array}{l}a = 2\\b = -3\\c = 2\end{array} \right.\) 

`-> a + b + c = 2 - 3 + 2 = 1`