簡約 1.017ln(500/300)-0.287ln(650/100)

解

簡約

1.017 \cdot ln (\frac{500}{300}) - 0.287 \cdot ln (\frac{650}{100})

ln (0.98245 \dots)

十進法表記

- 0.01769 \dots

解答ステップ

1.017 ln (\frac{500}{300}) - 0.287 ln (\frac{650}{100})

対数の規則を適用する:

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

1.017 ln (\frac{500}{300}) = ln ((\frac{500}{300})^{1.017})

= ln ((\frac{500}{300})^{1.017}) - 0.287 ln (\frac{650}{100})

対数の規則を適用する:

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

0.287 ln (\frac{650}{100}) = ln ((\frac{650}{100})^{0.287})

= ln ((\frac{500}{300})^{1.017}) - ln ((\frac{650}{100})^{0.287})

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 ((\frac{500}{300})^{1.017}) - ln ((\frac{650}{100})^{0.287}) = ln (\frac{( \frac{500}{300} ) ^{1.017}}{( \frac{650}{100} ) ^{0.287}})

= ln (\frac{( \frac{500}{300} ) ^{1.017}}{( \frac{650}{100} ) ^{0.287}})

\frac{( \frac{500}{300} ) ^{1.017}}{( \frac{650}{100} ) ^{0.287}} = 0.98245 \dots

= ln (0.98245 \dots)