Đáp án:

$\begin{array}{l}
B2)\\
a){5.2^{x - 2}} + {2^x} = 288\\
 \Leftrightarrow {5.2^x}:{2^2} + {2^x} = 288\\
 \Leftrightarrow {2^x}.\left( {\frac{5}{4} + 1} \right) = 288\\
 \Leftrightarrow {2^x}.\frac{9}{4} = 288\\
 \Leftrightarrow {2^x} = 128\\
 \Leftrightarrow {2^x} = {2^7}\\
 \Leftrightarrow x = 7\\
Vậy\,x = 7\\
b)8 < {2^x} < {4^7}\\
 \Leftrightarrow {2^3} < {2^x} < {2^{14}}\\
 \Leftrightarrow 3 < x < 14\\
 \Leftrightarrow x \in \left\{ {4;5;6;7;8;9;10;11;12;13} \right\}\\
Vậy\,x \in \left\{ {4;5;6;7;8;9;10;11;12;13} \right\}\\
c){2.3^x} = {10.3^{12}} + {8.27^4}\\
 \Leftrightarrow {2.3^x} = {10.3^{12}} + {8.3^{12}}\\
 \Leftrightarrow {2.3^x} = {18.3^{12}}\\
 \Leftrightarrow {2.3^x} = {2.3^{2 + 12}}\\
 \Leftrightarrow x = 2 + 12 = 14\\
Vậy\,x = 14\\
d)x = {x^9}\\
 \Leftrightarrow {x^9} - x = 0\\
 \Leftrightarrow x.\left( {{x^8} - 1} \right) = 0\\
 \Leftrightarrow \left[ \begin{array}{l}
x = 0\\
{x^8} = 1
\end{array} \right.\\
 \Leftrightarrow \left[ \begin{array}{l}
x = 0\\
x = 1\\
x =  - 1
\end{array} \right.\\
Vậy\,x = 0;x = 1;x =  - 1\\
e){\left( {x - 2} \right)^7} = {\left( {x - 2} \right)^4}\\
 \Leftrightarrow {\left( {x - 2} \right)^4}.\left( {{{\left( {x - 2} \right)}^3} - 1} \right) = 0\\
 \Leftrightarrow \left[ \begin{array}{l}
x - 2 = 0\\
{\left( {x - 2} \right)^3} = 1
\end{array} \right.\\
 \Leftrightarrow \left[ \begin{array}{l}
x = 2\\
x - 2 = 1
\end{array} \right.\\
 \Leftrightarrow \left[ \begin{array}{l}
x = 2\\
x = 3
\end{array} \right.\\
Vậy\,x = 2;x = 3\\
B3)\\
a)M = 2 + {2^2} + {2^3} + ... + {2^{50}}\\
 \Leftrightarrow 2M = {2^2} + {2^3} + {2^4} + ... + {2^{51}}\\
 \Leftrightarrow 2M - M = {2^{51}} - 2\\
 \Leftrightarrow M = {2^{51}} - 2\\
Vậy\,M = {2^{51}} - 2\\
b){2^{51}} - 2 > {2^{51}}\\
 \Leftrightarrow M > {2^{51}}\\
c)M = {2^{51}} - 2 = 2.\left( {{2^{50}} - 1} \right) \vdots 2
\end{array}$

Vậy M là số chẵn