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受欢迎的代数 >

x^{0.5log_{10}(x)}=0.01x^2

解答

x^{0.5 l o g_{10} (x)} = 0.01 x^{2}

解答

x = 1 0^{2 + 1.0 E - 15}, x = 1 0^{2 - 1.0 E - 15}

+1

十进制

x = 100.00000 \dots, x = 99.99999 \dots

求解步骤

x^{0.5 l o g_{10} (x)} = 0.01 x^{2}

使用对数运算法则

0.5 lo g_{10} (x) lo g_{10} (x) = lo g_{10} (0.01) + 2 lo g_{10} (x)

用

lo g_{10} (x) = u

改写方程式

0.5 uu = lo g_{10} (0.01) + 2 u

解

0.5 uu = lo g_{10} (0.01) + 2 u : u = 2 + 1.0 E - 15, u = 2 - 1.0 E - 15

u = 2 + 1.0 E - 15, u = 2 - 1.0 E - 15

代回

u = lo g_{10} (x)

，求解

x

解

lo g_{10} (x) = 2 + 1.0 E - 15 : x = 1 0^{2 + 1.0 E - 15}

解

lo g_{10} (x) = 2 - 1.0 E - 15 : x = 1 0^{2 - 1.0 E - 15}

x = 1 0^{2 + 1.0 E - 15}, x = 1 0^{2 - 1.0 E - 15}

验证解:

x = 1 0^{2 + 1.0 E - 15}

真

, x = 1 0^{2 - 1.0 E - 15}

真

解为

x = 1 0^{2 + 1.0 E - 15}, x = 1 0^{2 - 1.0 E - 15}

作图

流行的例子

solvefor x,z=ln(2x+3y)

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