Đáp án:
B1:
$\begin{array}{l}
a) \Leftrightarrow x = 1\\
b)x = \dfrac{{ - 1}}{{15}}\\
c)\left[ \begin{array}{l}
x = - 0,3\\
x = - 1,3
\end{array} \right.
\end{array}$
B2:
$\begin{array}{l}
a)\dfrac{{27}}{4}\\
b)80\\
c)243\\
d)3125
\end{array}$
Giải thích các bước giải:
B1:
$\begin{array}{l}
a){27^x}:{3^x} = 9\\
\Leftrightarrow {3^{3x}}:{3^x} = {3^2}\\
\Leftrightarrow {3^{2x}} = {3^2}\\
\Leftrightarrow 2x = 2\\
\Leftrightarrow x = 1\\
b){\left( {x + \dfrac{2}{5}} \right)^3} = \dfrac{1}{{27}}\\
\Leftrightarrow {\left( {x + \dfrac{2}{5}} \right)^3} = {\left( {\dfrac{1}{3}} \right)^3}\\
\Leftrightarrow x + \dfrac{2}{5} = \dfrac{1}{3}\\
\Leftrightarrow x = \dfrac{{ - 1}}{{15}}\\
c){\left( {x + 0,8} \right)^2} = 0,25\\
\Leftrightarrow \left[ \begin{array}{l}
x + 0,8 = 0,5\\
x + 0,8 = - 0,5
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = - 0,3\\
x = - 1,3
\end{array} \right.
\end{array}$
B2:
$\begin{array}{l}
a)\dfrac{{{4^{10}}{{.3}^{15}}}}{{{2^{22}}{{.27}^4}}} = \dfrac{{{2^{20}}{{.3}^{15}}}}{{{2^{22}}{{.3}^{12}}}} = \dfrac{{{3^3}}}{{{2^2}}} = \dfrac{{27}}{4}\\
b)\dfrac{{0,{8^5}}}{{0,{4^6}}} = {\left( {\dfrac{{0,8}}{{0,4}}} \right)^5}.\dfrac{1}{{0,4}} = {2^5}.\dfrac{{10}}{4} = 80\\
c)\dfrac{{{{45}^{10}}{{.5}^{20}}}}{{{{75}^{15}}}} = \dfrac{{{3^{20}}{{.5}^{10}}{{.5}^{20}}}}{{{3^{15}}{{.5}^{30}}}} = {3^5} = 243\\
d)\dfrac{{{{20}^5}{{.5}^{10}}}}{{{{100}^5}}} = \dfrac{{{{20}^5}{{.5}^{10}}}}{{{{20}^5}{{.5}^5}}} = {5^5} = 3125
\end{array}$
