Đáp án:
\[x \in \left\{ {0;1;2;3;4;5} \right\}\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
{5^x}{.5^{x + 1}}{.5^{x + 2}} \le 1000....00:{2^{18}}\,\,\,\,\,\,\,\,\left( {18\,\,c/s\,\,0} \right)\\
\Leftrightarrow {5^{x + \left( {x + 1} \right) + \left( {x + 2} \right)}} \le {10^{18}}:{2^{18}}\\
\Leftrightarrow {5^{3x + 3}} \le {\left( {2.5} \right)^{18}}:{2^{18}}\\
\Leftrightarrow {5^{5x + 3}} \le {2^{18}}{.5^{18}}:{2^{18}}\\
\Leftrightarrow {5^{3x + 3}} \le {5^{18}}\\
\Leftrightarrow 3x + 3 \le 18\\
\Leftrightarrow 3x \le 18 - 3\\
\Leftrightarrow 3x \le 15\\
\Leftrightarrow x \le 15:3\\
\Leftrightarrow x \le 5\\
\Rightarrow x \in \left\{ {0;1;2;3;4;5} \right\}
\end{array}\)
Vậy \(x \in \left\{ {0;1;2;3;4;5} \right\}\)
