簡約 (ln(2))/(ln(2)-2ln(3))

解

簡約

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

\frac{ln ( 2 )}{ln ( \frac{2}{9} )}

十進法表記

- 0.46084 \dots

解答ステップ

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

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

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

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

3^{2} = 9

= \frac{ln ( 2 )}{ln ( \frac{2}{9} )}