5^{2x-1}=\sqrt[3]{25^{x^2-1/4}}

解

5^{2 x - 1} = 3 2 5^{x^{2} - \frac{1}{4}}

x = \frac{5}{2}, x = \frac{1}{2}

十進法表記

x = 2.5, x = 0.5

解答ステップ

5^{2 x - 1} = 3 2 5^{x^{2} - \frac{1}{4}}

指数の規則を適用する

2 x - 1 = \frac{2}{3} (x^{2} - \frac{1}{4})

解く

2 x - 1 = \frac{2}{3} (x^{2} - \frac{1}{4}) : x = \frac{5}{2}, x = \frac{1}{2}

x = \frac{5}{2}, x = \frac{1}{2}