簡約 ln(94.72)0.42+ln(138.96)0.58

解

簡約

ln (94.72) 0.42 + ln (138.96) 0.58

ln (118.29914 \dots)

十進法表記

4.77321 \dots

解答ステップ

ln (94.72) \cdot 0.42 + ln (138.96) \cdot 0.58

対数の規則を適用する:

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

0.42 ln (94.72) = ln (94.7 2^{0.42})

= ln (94.7 2^{0.42}) + 0.58 ln (138.96)

対数の規則を適用する:

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

0.58 ln (138.96) = ln (138.9 6^{0.58})

= ln (94.7 2^{0.42}) + ln (138.9 6^{0.58})

対数の規則を適用する:

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

ln (94.7 2^{0.42}) + ln (138.9 6^{0.58}) = ln (94.7 2^{0.42} \cdot 138.9 6^{0.58})

= ln (94.7 2^{0.42} \cdot 138.9 6^{0.58})

94.7 2^{0.42} \cdot 138.9 6^{0.58} = 118.29914 \dots

= ln (118.29914 \dots)