簡約 (ln(7))/(2ln(3)-ln(7))

解

簡約

\frac{ln ( 7 )}{2 ln ( 3 ) - ln ( 7 )}

\frac{ln ( 7 )}{ln ( \frac{9}{7} )}

十進法表記

7.74293 \dots

解答ステップ

\frac{ln ( 7 )}{2 ln ( 3 ) - ln ( 7 )}

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 ( 7 )}{ln ( 3 ^{2} ) - ln ( 7 )}

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 (7) = ln (\frac{3 ^{2}}{7})

= \frac{ln ( 7 )}{ln ( \frac{3 ^{2}}{7} )}

3^{2} = 9

= \frac{ln ( 7 )}{ln ( \frac{9}{7} )}