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受欢迎的代数 >

8x-4=5x^{0.9}

解答

8 x - 4 = 5 x^{0.9}

解答

x = 1.28109 \dots

求解步骤

8 x - 4 = 5 x^{0.9}

使用以下的指数特性

: a^{n} = (a^{\frac{1}{m}})^{(n \cdot m)}

x^{0.9} = (x^{\frac{1}{10}})^{(0.9 \cdot 10)}

8 (x^{\frac{1}{10}})^{10} - 4 = 5 (x^{\frac{1}{10}})^{9}

用

x^{\frac{1}{10}} = u

改写方程式

8 u^{10} - 4 = 5 u^{9}

解

8 u^{10} - 4 = 5 u^{9} : u \approx 1.02508 \dots, u \approx - 0.88446 \dots

u \approx 1.02508 \dots, u \approx - 0.88446 \dots

代回

u = x^{\frac{1}{10}}

，求解

x

解

x^{\frac{1}{10}} = 1.02508 \dots : x = 1.28109 \dots

解

x^{\frac{1}{10}} = - 0.88446 \dots : x \in R

无解

x = 1.28109 \dots

验证解:

x = 1.28109 \dots

真

解是

x = 1.28109 \dots

作图

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