Cho

D

- Hướng dẫn giải

 Đáp án D

Ta có:

$a{\log }_{2}3+b{\log }_{6}2+c{\log }_{6}3=5\iff {\log }_6{2}^b+{\log }_6{3}^c={\log }_2{2}^5-{\log }_2{3}^a\iff {\log }_6{2}^b{3}^c={\log }_2\frac{2^5}{3^a}$

Đặt $\left\{\begin{array}{l}t={\log }_6{2}^b{3}^c\\ t={\log }_2\frac{2^5}{3^a}\end{array}\right.\iff \left\{\begin{array}{l}{2}^b{3}^c=6^t\\ \frac{2^5}{3^a}=2^t\end{array}\right.\iff \left\{\begin{array}{l}{2}^b{3}^c=6^t\\ 2^5=2^t{3}^a\end{array}\right.\iff \left\{\begin{array}{l}a=0\\ t=5\\ b=c=5\end{array}\right.$(vì a, b, c là các số tự nhiên)