Chọn phương án C.

• \(\log_5a=5\Leftrightarrow a=5^5\)
• \(\log_3b=\dfrac{2}{3}\Leftrightarrow b=3^{\tfrac{2}{3}}\)

Khi đó $$\begin{aligned}
I&=2\log_6\left[\log_5(5a)\right]+\log_{\tfrac{1}{9}}b^3\\
&=2\log_6\left[\log_5\left(5\cdot5^5\right)\right]+\log_{\tfrac{1}{9}}\left(3^{\tfrac{2}{3}}\right)^3\\
&=2\log_6\left[\log_55^6\right]+\log_{3^{-2}}3^2\\
&=2\log_6\left[6\log_55\right]+\dfrac{2}{-2}\log_33\\
&=2\log_66-\log_33=1.
\end{aligned}$$