簡約 (1/(0.143))ln((5*10^9)/(34000))

解

簡約

(\frac{1}{0.143}) ln (\frac{5 \cdot 1 0 ^{9}}{34000})

\frac{1}{0.143} (ln (5000000000) - ln (34000))

十進法表記

83.20690 \dots

解答ステップ

(\frac{1}{0.143}) ln (\frac{5 \cdot 1 0 ^{9}}{34000})

対数の規則を適用する:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{5 \cdot 1 0 ^{9}}{34000}) = ln (5 \cdot 1 0^{9}) - ln (34000)

= \frac{1}{0.143} (ln (1 0^{9} \cdot 5) - ln (34000))

ln (5 \cdot 1 0^{9}) = ln (5000000000)

= \frac{1}{0.143} (ln (5000000000) - ln (34000))