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受欢迎的代数 >

x=100x^{0.72}

解答

x = 100 x^{0.72}

解答

x = 0, x = 1000000 \cdot 10 0^{\frac{4}{7}}

+1

十进制

x = 0, x = 13894954.94373 \dots

求解步骤

x = 100 x^{0.72}

使用以下的指数特性

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

x^{0.72} = (x^{\frac{1}{25}})^{(0.72 \cdot 25)}

(x^{\frac{1}{25}})^{25} = 100 (x^{\frac{1}{25}})^{18}

用

x^{\frac{1}{25}} = u

改写方程式

u^{25} = 100 u^{18}

解

u^{25} = 100 u^{18} : u = 0, u = 7100

u = 0, u = 7100

代回

u = x^{\frac{1}{25}}

，求解

x

解

x^{\frac{1}{25}} = 0 : x = 0

解

x^{\frac{1}{25}} = 7100 : x = 1000000 \cdot 10 0^{\frac{4}{7}}

x = 0, x = 1000000 \cdot 10 0^{\frac{4}{7}}

验证解:

x = 0

真

, x = 1000000 \cdot 10 0^{\frac{4}{7}}

真

解为

x = 0, x = 1000000 \cdot 10 0^{\frac{4}{7}}

作图

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