Đáp án:
\(\begin{array}{l}
a)\,\,x = 1\\
b)\,\,\frac{{15\sqrt {10} - 10}}{{20}}
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\,\,\,\frac{1}{9}{.27^x} = {3^x}\\
\Leftrightarrow {27^x} = {9.3^x} \Leftrightarrow {\left( {{3^3}} \right)^x} = {3^2}{.3^x}\\
\Leftrightarrow {3^{3x}} = {3^{x + 2}} \Leftrightarrow 3x = x + 2\\
\Leftrightarrow 2x = 2 \Leftrightarrow x = 1.\\
b)\,\,\,\sqrt {0,1} .\sqrt {225} - \sqrt {\frac{1}{4}} \\
= \sqrt {\frac{1}{{10}}} .\sqrt {{{15}^2}} - \sqrt {{{\left( {\frac{1}{2}} \right)}^2}} \\
= \frac{{15}}{{\sqrt {10} }} - \frac{1}{2} = \frac{{15 - \sqrt {10} }}{{2\sqrt {10} }} = \frac{{15\sqrt {10} - 10}}{{20}}.
\end{array}\)
