Ta có: \(\left(13.3^{x-2}-3^x\right)\div2=162\)
\(\Leftrightarrow13.3^{x-2}-3^{x-2+2}=162.2\)
\(\Leftrightarrow13.3^{x-2}-3^2.3^{x-2}=324\)
\(\Leftrightarrow\left(13-9\right).3^{x-2}=324\)
\(\Leftrightarrow4.3^{x-2}=324\)
\(\Leftrightarrow3^{x-2}=\dfrac{324}{4}=81=3^4\)
\(\Leftrightarrow3^{x-2}=3^4\Leftrightarrow x-2=4\Leftrightarrow x=6\)
Vậy \(x=6\)