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Ta có:
$ \lg \left( {3C_m^2} \right) - \lg C_m^1 = 1\,\,\, \Leftrightarrow \,\,\,\frac{{3C_m^3}}{{C_m^1}} = 10 $ $ \begin{array}{l}
\Leftrightarrow \,\,\,3C_m^3 = 10C_m^1 & \Leftrightarrow \,\,\,{m^2} - 3m - 18 = 0
\Leftrightarrow \,\,\,m = 6 \vee m = - 3
\end{array} $
Chỉ có $ m = 6 $ là thích hợp
$ \begin{array}{l}
9{T_3} - {T_5} = 240\\
\Leftrightarrow \,\,9C_6^2{2^{x\left( {\frac{2}{3} + \frac{x}{2}} \right)}}{.2^{4\left( {\frac{{x - 1}}{2} - \frac{1}{2}} \right)}}{.2^{2\left( {\frac{{x - 1}}{2} - \frac{1}{3}} \right)}} = 240\\
\Leftrightarrow \,\,{9.2^{3x - 2}} - {2^{3x + 1}} = 16\,\,\,\, \Leftrightarrow \,\,\,{9.2^{3x\frac{1}{2}}} - {2^{3x}}.2 = 16\\
\Leftrightarrow \,\,{2^{3x}} = {2^{6\,\,\,}} \Leftrightarrow \,\,x = 2
\end{array} $
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