簡約 1/(4-2)ln(4/2)

解

簡約

\frac{1}{4 - 2} ln (\frac{4}{2})

\frac{ln ( 2 )}{2}

十進法表記

0.34657 \dots

解答ステップ

\frac{1}{4 - 2} ln (\frac{4}{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 (\frac{4}{2}) = ln (4) - ln (2)

= \frac{1}{4 - 2} (ln (4) - ln (2))

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot ( ln ( 4 ) - ln ( 2 ) )}{4 - 2}

1 \cdot (ln (4) - ln (2)) = ln (4) - ln (2)

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

数を引く:

4 - 2 = 2

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

ln (4) = 2 ln (2)

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

類似した元を足す:

2 ln (2) - ln (2) = ln (2)

= \frac{ln ( 2 )}{2}