化简 log_{25}(1/5)

解答

化简

lo g_{25} (\frac{1}{5})

- \frac{1}{2}

十进制

- 0.5

求解步骤

lo g_{25} (\frac{1}{5})

因式分解数字:

25 = 5^{2}

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

使用对数计算法则:

lo g_{a^{b}} (x) = \frac{1}{b} lo g_{a} (x), a > 0

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

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

\frac{1}{5} = 5^{- 1}

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

使用对数计算法则:

lo g_{a} (a^{b}) = b

lo g_{5} (5^{- 1}) = - 1

= \frac{1}{2} (- 1)

\frac{1}{2} (- 1) = - \frac{1}{2}

= - \frac{1}{2}

6 n + 8 = 1 - n

13 x - 1 = 9 x - 13

f a c t or a^{4} - 2 a^{2} b^{2} + b^{4}

\frac{x}{14} \geq 1 - \frac{x}{28}

f a c t or 2 (5 a - 1)^{\frac{3}{4}} + 7 a (5 a - 1)^{- \frac{1}{4}}