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Câu hỏi: Nghiệm của phương trình ${{5}^{x-1}}={{\left( \dfrac{1}{25} \right)}^{x}}$ nằm trong khoảng nào dưới đây?
A. $\left( -\dfrac{3}{2};-\dfrac{1}{2} \right).$
B. $\left( \dfrac{1}{2};1 \right).$
C. $\left( -\dfrac{1}{2};0 \right).$
D. $\left( 0;\dfrac{1}{2} \right).$
A. $\left( -\dfrac{3}{2};-\dfrac{1}{2} \right).$
B. $\left( \dfrac{1}{2};1 \right).$
C. $\left( -\dfrac{1}{2};0 \right).$
D. $\left( 0;\dfrac{1}{2} \right).$
${{5}^{x+1}}={{\left( \dfrac{1}{25} \right)}^{x}}\Leftrightarrow {{5}^{x-1}}={{5}^{-2x}}\Leftrightarrow x-1=-2x\Leftrightarrow x=\dfrac{1}{3}\in \left( 0;\dfrac{1}{2} \right)$.
Đáp án D.