化简 log_{10}(\sqrt[3]{0.01sqrt(0.1)})

解答

化简

lo g_{10} (3 0.01 0.1)

- \frac{5}{6}

十进制

- 0.83333 \dots

求解步骤

lo g_{10} (3 0.01 0.1)

3 0.01 0.1 = 0.0 1^{\frac{1}{3}} \cdot 1 0^{- \frac{1}{6}}

= lo g_{10} (0.0 1^{\frac{1}{3}} \cdot 1 0^{- \frac{1}{6}})

使用对数计算法则:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{10} (0.0 1^{\frac{1}{3}} \cdot 1 0^{- \frac{1}{6}}) = lo g_{10} (0.0 1^{\frac{1}{3}}) + lo g_{10} (1 0^{- \frac{1}{6}})

= lo g_{10} (0.0 1^{\frac{1}{3}}) + lo g_{10} (1 0^{- \frac{1}{6}})

lo g_{10} (0.0 1^{\frac{1}{3}}) = - \frac{2}{3}

= - \frac{2}{3} + lo g_{10} (1 0^{- \frac{1}{6}})

使用对数计算法则:

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

lo g_{10} (1 0^{- \frac{1}{6}}) = - \frac{1}{6}

= - \frac{2}{3} - \frac{1}{6}

- \frac{2}{3} - \frac{1}{6} = - \frac{5}{6}

= - \frac{5}{6}

s im pl i f y \frac{\frac{a - x}{a x}}{x - a}

\frac{63}{36}

s im pl i f y - 2 \times 3 x

s im pl i f y - 2 \times + 2

s im pl i f y 2 (x - 3)^{3} - 6 x + 13