Giải thích các bước giải:
\[\begin{array}{l}
1,\\
{3^x} = \frac{1}{{27}}\\
\Leftrightarrow {3^x} = \frac{1}{{{3^3}}}\\
\Leftrightarrow {3^x}{.3^3} = 1\\
\Leftrightarrow x + 3 = 0\\
\Leftrightarrow x = - 3\\
2,(x > 0)\\
{\log _2}x = - 3 \Leftrightarrow x = {2^{ - 3}} = \frac{1}{{{2^3}}} = \frac{1}{8}\\
4,\left( {x > 0} \right)\\
{\log _3}x < \frac{1}{2} \Leftrightarrow x < {3^{\frac{1}{2}}} \Leftrightarrow x < \sqrt 3 \\
\Rightarrow S = \left( {0;\sqrt 3 } \right)\\
5,\\
{4^{2x}} = {4^{{x^2}}}\\
\Leftrightarrow 2x = {x^2}\\
\Leftrightarrow \left[ \begin{array}{l}
x = 0\\
x = 2
\end{array} \right.
\end{array}\]