簡約-364/1740-1.144-ln(1.10066)+0.5ln(2)

解

簡約

- \frac{364}{1740} - 1.144 - ln (1.10066) + 0.5 ln (2)

- \frac{91}{435} - 1.144 + ln (1.28487 \dots)

十進法表記

- 1.10253 \dots

解答ステップ

- \frac{364}{1740} - 1.144 - ln (1.10066) + 0.5 ln (2)

対数の規則を適用する:

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

0.5 ln (2) = ln (2^{0.5})

= - \frac{364}{1740} - 1.144 - ln (1.10066) + ln (2^{0.5})

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^{0.5}) - ln (1.10066) = ln (\frac{2 ^{0.5}}{1.10066})

= - \frac{364}{1740} - 1.144 + ln (\frac{2 ^{0.5}}{1.10066})

\frac{2 ^{0.5}}{1.10066} = 1.28487 \dots

= - \frac{364}{1740} - 1.144 + ln (1.28487 \dots)

キャンセル

\frac{364}{1740} : \frac{91}{435}

= - \frac{91}{435} - 1.144 + ln (1.28487 \dots)