簡約 8.314(59+273)ln(0.286)-ln(1.99*10^{11})

解

簡約

8.314 (59 + 273) ln (0.286) - ln (1.99 \cdot 1 0^{11})

2760.248 ln (0.286) - ln (1.99) - 11 ln (10)

十進法表記

- 3481.19418 \dots

解答ステップ

8.314 (59 + 273) ln (0.286) - ln (1.99 \cdot 1 0^{11})

対数の規則を適用する:

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

ln (1.99 \cdot 1 0^{11}) = ln (1.99) + ln (1 0^{11})

= 8.314 ln (0.286) (59 + 273) - (ln (1.99) + ln (1 0^{11}))

対数の規則を適用する:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (1 0^{11}) = 11 ln (10)

= 8.314 (59 + 273) ln (0.286) - (ln (1.99) + 11 ln (10))

8.314 (59 + 273) ln (0.286) = 2760.248 ln (0.286)

= 2760.248 ln (0.286) - (11 ln (10) + ln (1.99))

- (ln (1.99) + 11 ln (10)) : - ln (1.99) - 11 ln (10)

= 2760.248 ln (0.286) - ln (1.99) - 11 ln (10)