簡約 (-6ln(8))/(ln(8)-ln(5))

解

簡約

\frac{- 6 ln ( 8 )}{ln ( 8 ) - ln ( 5 )}

- \frac{18 ln ( 2 )}{ln ( \frac{8}{5} )}

十進法表記

- 26.54585 \dots

解答ステップ

\frac{- 6 ln ( 8 )}{ln ( 8 ) - ln ( 5 )}

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 (8) - ln (5) = ln (\frac{8}{5})

= \frac{- 6 ln ( 8 )}{ln ( \frac{8}{5} )}

分数の規則を適用する:

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

= - \frac{6 ln ( 8 )}{ln ( \frac{8}{5} )}

簡素化

ln (8) : 3 ln (2)

= - \frac{6 \cdot 3 ln ( 2 )}{ln ( \frac{8}{5} )}

数を乗じる:

6 \cdot 3 = 18

= - \frac{18 ln ( 2 )}{ln ( \frac{8}{5} )}