簡約 0.491ln(22)-0.491ln(20)

解

簡約

0.491 \cdot ln (22) - 0.491 \cdot ln (20)

ln (1.04790 \dots)

十進法表記

0.04679 \dots

解答ステップ

0.491 ln (22) - 0.491 ln (20)

対数の規則を適用する:

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

0.491 ln (22) = ln (2 2^{0.491})

= ln (2 2^{0.491}) - 0.491 ln (20)

対数の規則を適用する:

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

0.491 ln (20) = ln (2 0^{0.491})

= ln (2 2^{0.491}) - ln (2 0^{0.491})

対数の規則を適用する:

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

ln (2 2^{0.491}) - ln (2 0^{0.491}) = ln (\frac{2 2 ^{0.491}}{2 0 ^{0.491}})

= ln (\frac{2 2 ^{0.491}}{2 0 ^{0.491}})

\frac{2 2 ^{0.491}}{2 0 ^{0.491}} = 1.04790 \dots

= ln (1.04790 \dots)