簡約 1.1ln(670/970)-(8.314)/(28.97)ln(1/4)

解

簡約

1.1 \cdot ln (\frac{670}{970}) - \frac{8.314}{28.97} \cdot ln (\frac{1}{4})

ln (0.99086 \dots)

十進法表記

- 0.00917 \dots

解答ステップ

1.1 ln (\frac{670}{970}) - \frac{8.314}{28.97} ln (\frac{1}{4})

対数の規則を適用する:

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

1.1 ln (\frac{670}{970}) = ln ((\frac{670}{970})^{1.1})

= ln ((\frac{670}{970})^{1.1}) - \frac{8.314}{28.97} ln (\frac{1}{4})

対数の規則を適用する:

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

\frac{8.314}{28.97} ln (\frac{1}{4}) = ln ((\frac{1}{4})^{\frac{8.314}{28.97}})

= ln ((\frac{670}{970})^{1.1}) - ln ((\frac{1}{4})^{\frac{8.314}{28.97}})

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{670}{970})^{1.1}) - ln ((\frac{1}{4})^{\frac{8.314}{28.97}}) = ln \frac{( \frac{670}{970} ) ^{1.1}}{( \frac{1}{4} ) ^{\frac{8.314}{28.97}}}

= ln \frac{( \frac{670}{970} ) ^{1.1}}{( \frac{1}{4} ) ^{\frac{8.314}{28.97}}}

\frac{( \frac{670}{970} ) ^{1.1}}{( \frac{1}{4} ) ^{\frac{8.314}{28.97}}} = 0.99086 \dots

= ln (0.99086 \dots)