簡約 (-2ln(6))/(2ln(3)-ln(6))

解

簡約

\frac{- 2 ln ( 6 )}{2 ln ( 3 ) - ln ( 6 )}

- \frac{2 ln ( 6 )}{ln ( \frac{3}{2} )}

十進法表記

- 8.83804 \dots

解答ステップ

\frac{- 2 ln ( 6 )}{2 ln ( 3 ) - ln ( 6 )}

対数の規則を適用する:

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

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

= \frac{- 2 ln ( 6 )}{ln ( 3 ^{2} ) - ln ( 6 )}

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 (3^{2}) - ln (6) = ln (\frac{3 ^{2}}{6})

= \frac{- 2 ln ( 6 )}{ln ( \frac{3 ^{2}}{6} )}

\frac{3 ^{2}}{6} = \frac{3}{2}

= \frac{- 2 ln ( 6 )}{ln ( \frac{3}{2} )}

分数の規則を適用する:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{2 ln ( 6 )}{ln ( \frac{3}{2} )}