簡約 (0-ln(2))-(2ln(2)-ln(3))

解

簡約

(0 - ln (2)) - (2 ln (2) - ln (3))

- ln (\frac{8}{3})

十進法表記

- 0.98082 \dots

解答ステップ

(0 - ln (2)) - (2 ln (2) - ln (3))

対数の規則を適用する:

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

2 ln (2) = ln (2^{2})

= (- ln (2) + 0) - (ln (2^{2}) - ln (3))

対数の規則を適用する:

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

ln (2^{2}) - ln (3) = ln (\frac{2 ^{2}}{3})

= 0 - ln (2) - ln (\frac{2 ^{2}}{3})

2^{2} = 4

= 0 - ln (2) - ln (\frac{4}{3})

- ln (2) - ln (\frac{4}{3})

を書き換え

- (ln (2) + ln (\frac{4}{3}))

= 0 - (ln (2) + ln (\frac{4}{3}))

対数の規則を適用する:

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

ln (2) + ln (\frac{4}{3}) = ln (2 \cdot \frac{4}{3})

= 0 - ln (2 \cdot \frac{4}{3})

2 \cdot \frac{4}{3} = \frac{8}{3}

= 0 - ln (\frac{8}{3})

0 - ln (\frac{8}{3}) = - ln (\frac{8}{3})

= - ln (\frac{8}{3})