簡約 ln(9/7)*500/6

解

簡約

ln (\frac{9}{7}) \cdot \frac{500}{6}

\frac{250 ( 2 ln ( 3 ) - ln ( 7 ) )}{3}

十進法表記

20.94286 \dots

解答ステップ

ln (\frac{9}{7}) \frac{500}{6}

対数の規則を適用する:

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

ln (\frac{9}{7}) = ln (9) - ln (7)

= \frac{500}{6} (ln (9) - ln (7))

分数を乗じる:

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

= \frac{500 ( ln ( 9 ) - ln ( 7 ) )}{6}

共通因数を約分する:

2

= \frac{250 ( ln ( 9 ) - ln ( 7 ) )}{3}

ln (9) = 2 ln (3)

= \frac{250 ( 2 ln ( 3 ) - ln ( 7 ) )}{3}