Chọn phương án A.

\(\begin{eqnarray*}
&\log_{\tfrac{1}{3}}^2x-5\log_3x+4&=0\\
\Leftrightarrow&\log_{3^{-1}}^2x-5\log_3x+4&=0\\
\Leftrightarrow&\left(-\log_3x\right)^2-5\log_3x+4&=0.\\
\Leftrightarrow&\log_3^2x-5\log_3x+4&=0.
\end{eqnarray*}\)

Đặt \(t=\log_3x\) (\(x>0\)), ta được phương trình $$\begin{aligned}
t^2-5t+4=0\Leftrightarrow&\left[\begin{array}{l}
t=1\\
t=4
\end{array}\right.\\
\Leftrightarrow&\left[\begin{array}{l}
\log_3x=1\\
\log_3x=4
\end{array}\right.\\
\Leftrightarrow&\left[\begin{array}{l}
x=3^1=3\\
x=3^4=81
\end{array}\right.
\end{aligned}$$
Vậy \(T=3+81=84\).