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受欢迎的代数 >

(log_{10}(10x))2-4log_{10}(10x)-5=0

解答

(lo g_{10} (10 x)) 2 - 4 lo g_{10} (10 x) - 5 = 0

解答

x = \frac{1}{1000 10}

+1

十进制

x = 0.00031 \dots

求解步骤

(lo g_{10} (10 x)) \cdot 2 - 4 lo g_{10} (10 x) - 5 = 0

同类项相加:

2 lo g_{10} (10 x) - 4 lo g_{10} (10 x) = - 2 lo g_{10} (10 x)

- 2 lo g_{10} (10 x) - 5 = 0

将

5

到右边

- 2 lo g_{10} (10 x) = 5

两边除以

- 2

lo g_{10} (10 x) = - \frac{5}{2}

使用对数运算法则

10 x = \frac{1}{100 10}

解

10 x = \frac{1}{100 10} : x = \frac{1}{1000 10}

x = \frac{1}{1000 10}

验证解:

x = \frac{1}{1000 10}

真

解是

x = \frac{1}{1000 10}

作图

流行的例子

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