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受欢迎的代数 >

(log_{10}(0.5x))^2+log_{10}(0.5x)-2<= 0

解答

(lo g_{10} (0.5 x))^{2} + lo g_{10} (0.5 x) - 2 \leq 0

解答

\frac{1}{50} \leq x \leq 20

+2

间隔符号

[\frac{1}{50}, 20]

十进制

0.02 \leq x \leq 20

求解步骤

(lo g_{10} (0.5 x))^{2} + lo g_{10} (0.5 x) - 2 \leq 0

化简

lo g_{10} (0.5 x)^{2} + lo g_{10} (0.5 x) - 2 \leq 0

令

u = lo g_{10} (0.5 x)

u^{2} + u - 2 \leq 0

u^{2} + u - 2 \leq 0 : - 2 \leq u \leq 1

- 2 \leq u \leq 1

u = lo g_{10} (0.5 x)

代回

- 2 \leq lo g_{10} (0.5 x) \leq 1

若

a \leq u \leq b

，则

a \leq u and u \leq b

- 2 \leq lo g_{10} (0.5 x) and lo g_{10} (0.5 x) \leq 1

- 2 \leq lo g_{10} (0.5 x) : x \geq \frac{1}{50}

lo g_{10} (0.5 x) \leq 1 : 0 < x \leq 20

合并区间

x \geq \frac{1}{50} and 0 < x \leq 20

合并重叠的区间

\frac{1}{50} \leq x \leq 20

作图

流行的例子

log_{1/2}(x^2-1)>= log_{1/2}(3x)

lo g_{\frac{1}{2}} (x^{2} - 1) \geq lo g_{\frac{1}{2}} (3 x)

3x+1<2*log_{2}(x+4)

3 x + 1 < 2 \cdot lo g_{2} (x + 4)

log_{10}(x-2)(3x^2-x-1)>0

lo g_{10} (x - 2) (3 x^{2} - x - 1) > 0

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

2 - lo g_{10} (4 x) \geq 0

log_{2}(x-1)>-1

lo g_{2} (x - 1) > - 1