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BPT
$\Leftrightarrow 3\left ( \frac{2}{3} \right )^{2x}+1 \ge 4\left ( \frac{2}{3} \right )^x$
$\Leftrightarrow \left[ {\left ( \frac{2}{3} \right )^x-1} \right]\left[ {3\left ( \frac{2}{3} \right )^x-1} \right] \ge 0$
$\Leftrightarrow \left[ {\left ( \frac{2}{3} \right )^x-1} \right]\left[ {\left ( \frac{2}{3} \right )^x-\frac{1}{3}} \right] \ge 0$
$\Leftrightarrow \left[ {\begin{matrix} \left ( \frac{2}{3} \right )^x \ge 1\\ \left ( \frac{2}{3} \right )^x \le \frac{1}{3} \end{matrix}} \right.$
$\Leftrightarrow \left[ {\begin{matrix} x \le 0\\ x \ge \log_{2/3}(1/3) \end{matrix}}
\right.$
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