Giải phương trình $5^{x^{2}-x+7}=125^{2 x-1}$.

Q: Giải phương trình $5^{x^{2}-x+7}=125^{2 x-1}$.

<span class="math-tex">$\begin{array}{l}5^{x^{2}-x+7}=125^{2 x-1} \\\Leftrightarrow 5^{x^{2}-x+7}=\left(5^{3}\right)^{2 x-1} \\\Leftrightarrow 5^{x^{2}-x+7}=5^{6 x-3} \\\Leftrightarrow x^{2}-x+7=6 x-3 \\\Leftrightarrow x^{2}-7 x+10=0 \\\Leftrightarrow\left[\begin{array}{l}x=2 \\x=5\end{array}\right.\end{array}$</span>

Question

Accepted Answer

$\begin{array}{l}5^{x^{2}-x+7}=125^{2 x-1} \\Leftrightarrow 5^{x^{2}-x+7}=\left(5^{3}\right)^{2 x-1} \\Leftrightarrow 5^{x^{2}-x+7}=5^{6 x-3} \\Leftrightarrow x^{2}-x+7=6 x-3 \\Leftrightarrow x^{2}-7 x+10=0 \\Leftrightarrow\left[\begin{array}{l}x=2 \x=5\end{array}\right.\end{array}$

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