簡約 1.05ln(700/1450)+0.287ln(50/2)+50/573

解

簡約

1.05 ln (\frac{700}{1450}) + 0.287 ln (\frac{50}{2}) + \frac{50}{573}

ln (1.17253 \dots) + \frac{50}{573}

十進法表記

0.24642 \dots

解答ステップ

1.05 ln (\frac{700}{1450}) + 0.287 ln (\frac{50}{2}) + \frac{50}{573}

対数の規則を適用する:

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

1.05 ln (\frac{700}{1450}) = ln ((\frac{700}{1450})^{1.05})

= ln ((\frac{700}{1450})^{1.05}) + 0.287 ln (\frac{50}{2}) + \frac{50}{573}

対数の規則を適用する:

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

0.287 ln (\frac{50}{2}) = ln ((\frac{50}{2})^{0.287})

= ln ((\frac{700}{1450})^{1.05}) + ln ((\frac{50}{2})^{0.287}) + \frac{50}{573}

対数の規則を適用する:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln ((\frac{700}{1450})^{1.05}) + ln ((\frac{50}{2})^{0.287}) = ln ((\frac{50}{2})^{0.287} (\frac{700}{1450})^{1.05})

= ln ((\frac{50}{2})^{0.287} (\frac{700}{1450})^{1.05}) + \frac{50}{573}

(\frac{700}{1450})^{1.05} (\frac{50}{2})^{0.287} = 1.17253 \dots

= ln (1.17253 \dots) + \frac{50}{573}