\(100< 5^{2x-1}< 5^6\Rightarrow125\le5^{2x-1}\le3^5\Leftrightarrow5^3\le5^{2x-1}\le5^3\)
\(\Leftrightarrow3\le2x-1\le5\Leftrightarrow4\le2x\le6\Leftrightarrow2\le x\le3\text{ nên: x=3 hoặc x=2}\)
100 < 52x - 1 ≤ 56
<=> 52 . 4 < 52x - 1 ≤ 56
<=> 52x - 1 \(\in\) { 53; 54; 55; 56 }
<=> 2x - 1 \(\in\) { 3; 4; 5; 6 }
<=> x \(\in\) { 2; 5/2; 3; 7/2 }
Vậy x \(\in\) {2; 5/2; 3; 7/2 }