簡約 ln(64e^3)-ln(4e)

解

簡約

ln (64 e^{3}) - ln (4 e)

4 ln (2) + 2

十進法表記

4.77258 \dots

解答ステップ

ln (64 e^{3}) - ln (4 e)

対数の規則を適用する:

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

ln (64 e^{3}) = ln (64) + ln (e^{3}), ln (4 e) = ln (4) + ln (e)

= ln (64) + ln (e^{3}) - (ln (4) + ln (e))

対数の規則を適用する:

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

ln (e^{3}) = 3 ln (e)

= ln (64) + 3 ln (e) - (ln (4) + ln (e))

3 ln (e) = 3

- (ln (4) + ln (e)) = - (2 ln (2) + 1)

= ln (64) + 3 - (2 ln (2) + 1)

ln (64) = 6 ln (2)

= 6 ln (2) + 3 - (2 ln (2) + 1)

- (2 ln (2) + 1) : - 2 ln (2) - 1

= 6 ln (2) + 3 - 2 ln (2) - 1

簡素化

6 ln (2) + 3 - 2 ln (2) - 1 : 4 ln (2) + 2

= 4 ln (2) + 2