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受欢迎的代数 >

(log_{10}(x^3))/3 =(log_{10}(x))^3

解答

\frac{lo g _{10} ( x ^{3} )}{3} = (lo g_{10} (x))^{3}

解答

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

+1

十进制

x = 1, x = 0.1, x = 10

求解步骤

\frac{lo g _{10} ( x ^{3} )}{3} = (lo g_{10} (x))^{3}

在两边乘以

3

\frac{lo g _{10} ( x ^{3} )}{3} \cdot 3 = (lo g_{10} (x))^{3} \cdot 3

化简

lo g_{10} (x^{3}) = 3 lo g_{10} (x)^{3}

使用对数运算法则

lo g_{10} (x) = lo g_{10} (x)^{3}

用

lo g_{10} (x) = u

改写方程式

u = u^{3}

解

u = u^{3} : u = 0, u = - 1, u = 1

u = 0, u = - 1, u = 1

代回

u = lo g_{10} (x)

，求解

x

解

lo g_{10} (x) = 0 : x = 1

解

lo g_{10} (x) = - 1 : x = \frac{1}{10}

解

lo g_{10} (x) = 1 : x = 10

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

验证解:

x = 1

真

, x = \frac{1}{10}

真

, x = 10

真

解为

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

作图

流行的例子

12.4=-log_{10}(x)

12.4 = - lo g_{10} (x)

lo g_{2} (x - 3) = 5

-3log_{7}(m-4)=-6

- 3 lo g_{7} (m - 4) = - 6

lo g_{\frac{1}{5}} (x) = 2

log_{2}(x^2-3x+4)=3

lo g_{2} (x^{2} - 3 x + 4) = 3