簡約 (ln(6)+ln(2))/(log_{10)(6)+log_{10}(2)}

解

簡約

\frac{ln ( 6 ) + ln ( 2 )}{lo g _{10} ( 6 ) + lo g _{10} ( 2 )}

\frac{ln ( 12 )}{lo g _{10} ( 12 )}

十進法表記

2.30258 \dots

解答ステップ

\frac{ln ( 6 ) + ln ( 2 )}{lo g _{10} ( 6 ) + lo g _{10} ( 2 )}

対数の規則を適用する:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (6) + ln (2) = ln (6 \cdot 2)

= \frac{ln ( 6 \cdot 2 )}{lo g _{10} ( 6 ) + lo g _{10} ( 2 )}

数を乗じる:

6 \cdot 2 = 12

= \frac{ln ( 12 )}{lo g _{10} ( 6 ) + lo g _{10} ( 2 )}

対数の規則を適用する:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{10} (6) + lo g_{10} (2) = lo g_{10} (6 \cdot 2)

= \frac{ln ( 12 )}{lo g _{10} ( 6 \cdot 2 )}

数を乗じる:

6 \cdot 2 = 12

= \frac{ln ( 12 )}{lo g _{10} ( 12 )}