簡約 ln((4.6710^{22})/(510^{22)})

解

簡約

ln (\frac{4.67 \cdot 1 0 ^{22}}{5 \cdot 1 0 ^{22}})

- ln (5) + ln (4.67)

十進法表記

- 0.06827 \dots

解答ステップ

ln (\frac{4.67 \cdot 1 0 ^{22}}{5 \cdot 1 0 ^{22}})

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{4.67 \cdot 1 0 ^{22}}{5 \cdot 1 0 ^{22}}) = ln (4.67 \cdot 1 0^{22}) - ln (5 \cdot 1 0^{22})

= ln (1 0^{22} \cdot 4.67) - ln (1 0^{22} \cdot 5)

対数の規則を適用する:

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

ln (4.67 \cdot 1 0^{22}) = ln (4.67) + ln (1 0^{22}), ln (5 \cdot 1 0^{22}) = ln (5) + ln (1 0^{22})

= ln (4.67) + ln (1 0^{22}) - (ln (5) + ln (1 0^{22}))

対数の規則を適用する:

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

ln (1 0^{22}) = 22 ln (10)

= ln (4.67) + 22 ln (10) - (ln (5) + 22 ln (10))

対数の規則を適用する:

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

ln (1 0^{22}) = 22 ln (10)

= ln (4.67) + 22 ln (10) - (ln (5) + 22 ln (10))

- (ln (5) + 22 ln (10)) : - ln (5) - 22 ln (10)

= ln (4.67) + 22 ln (10) - ln (5) - 22 ln (10)

簡素化

ln (4.67) + 22 ln (10) - ln (5) - 22 ln (10) : - ln (5) + ln (4.67)

= - ln (5) + ln (4.67)