簡約 (ln(1/3))/(ln(6)-ln(3))

解

簡約

\frac{ln ( \frac{1}{3} )}{ln ( 6 ) - ln ( 3 )}

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

十進法表記

- 1.58496 \dots

解答ステップ

\frac{ln ( \frac{1}{3} )}{ln ( 6 ) - 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 (6) - ln (3) = ln (\frac{6}{3})

= \frac{ln ( \frac{1}{3} )}{ln ( \frac{6}{3} )}

数を割る:

\frac{6}{3} = 2

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

簡素化

ln (\frac{1}{3}) : - ln (3)

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

分数の規則を適用する:

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

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