化简 1/(1/25 ln(2/3))ln((16-20)/(5-20))

解答

化简

\frac{1}{\frac{1}{25} ln ( \frac{2}{3} )} ln (\frac{16 - 20}{5 - 20})

\frac{25 ( ln ( - 4 ) - ln ( - 15 ) )}{ln ( \frac{2}{3} )}

求解步骤

\frac{1}{\frac{1}{25} ln ( \frac{2}{3} )} ln (\frac{16 - 20}{5 - 20})

使用对数计算法则:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{16 - 20}{5 - 20}) = ln (16 - 20) - ln (5 - 20)

= \frac{1}{\frac{1}{25} ln ( \frac{2}{3} )} (ln (16 - 20) - ln (5 - 20))

\frac{1}{\frac{1}{25} ln ( \frac{2}{3} )} = \frac{25}{ln ( \frac{2}{3} )}

= \frac{25}{ln ( \frac{2}{3} )} (ln (16 - 20) - ln (5 - 20))

数字相减:

16 - 20 = - 4

= \frac{25}{ln ( \frac{2}{3} )} (ln (- 4) - ln (5 - 20))

数字相减:

5 - 20 = - 15

= \frac{25}{ln ( \frac{2}{3} )} (ln (- 4) - ln (- 15))

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{25 ( ln ( - 4 ) - ln ( - 15 ) )}{ln ( \frac{2}{3} )}

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