Đáp án:
$\begin{array}{l}
3)a){3^4} < \dfrac{1}{9}{.27^n} < {3^{10}}\\
\Rightarrow {3^4} < \dfrac{1}{{{3^2}}}.{\left( {{3^3}} \right)^n} < {3^{10}}\\
\Rightarrow {3^4} < {3^{3n - 2}} < {3^{10}}\\
\Rightarrow 4 < 3n - 2 < 10\\
\Rightarrow 6 < 3n < 12\\
\Rightarrow 2 < n < 4\\
Do:n \in Z\\
\Rightarrow n = 3\\
\text{Vậy}\,n = 3\\
b)\dfrac{{81}}{{{3^n}}} = 3\\
\Rightarrow \dfrac{{{3^4}}}{{{3^n}}} = 3\\
\Rightarrow {3^{4 - n}} = {3^1}\\
\Rightarrow 4 - n = 1\\
\Rightarrow n = 3\\
\text{Vậy}\,n = 3\\
4)\dfrac{{{6^3} + {{3.6}^2} + {3^3}}}{{ - 18}}\\
= \dfrac{{{2^3}{{.3}^3} + {{3.2}^2}{{.3}^2} + {3^3}}}{{ - 18}}\\
= \dfrac{{{3^3}\left( {{2^3} + {2^2} + 1} \right)}}{{ - 18}}\\
= \dfrac{{{3^3}.\left( {8 + 4 + 1} \right)}}{{ - {3^2}.2}}\\
= \dfrac{{3.13}}{{ - 2}}\\
= \dfrac{{ - 39}}{2}\\
5)\\
7;\left( { - 3} \right);6;\left( { - 14} \right)\\
Do:6.7 = 42 = \left( { - 3} \right).\left( { - 14} \right)\\
\Rightarrow 6.7 = \left( { - 3} \right).\left( { - 14} \right)\\
\Rightarrow \left\{ \begin{array}{l}
\dfrac{6}{{ - 3}} = \dfrac{{ - 14}}{7}\\
\dfrac{6}{{ - 14}} = \dfrac{{ - 3}}{7}\\
\dfrac{{ - 3}}{6} = \dfrac{7}{{ - 14}}\\
\dfrac{7}{{ - 3}} = \dfrac{{ - 14}}{6}
\end{array} \right.
\end{array}$
