簡約 ln^2(1/3)-(ln(1/3))^2

解

簡約

ln^{2} (\frac{1}{3}) - (ln (\frac{1}{3}))^{2}

- 2 ln^{2} (3)

十進法表記

- 2.41389 \dots

解答ステップ

ln^{2} (\frac{1}{3}) - (ln (\frac{1}{3}))^{2}

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^{2} (\frac{1}{3}) = ln^{2} (1) - ln^{2} (3)

= ln^{2} (1) - ln^{2} (3) - ln^{2} (\frac{1}{3})

ln^{2} (1) = 0

= 0 - ln^{2} (3) - ln^{2} (\frac{1}{3})

0 - ln^{2} (3) - ln^{2} (\frac{1}{3}) = - ln^{2} (3) - ln^{2} (\frac{1}{3})

= - ln^{2} (3) - ln^{2} (\frac{1}{3})

ln^{2} (\frac{1}{3}) = ln^{2} (3)

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

類似した元を足す:

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

= - 2 ln^{2} (3)