簡約 (eln(90)+ln(6))/(ln(3)+ln(20))

解

簡約

\frac{e ln ( 90 ) + ln ( 6 )}{ln ( 3 ) + ln ( 20 )}

\frac{e ln ( 90 ) + ln ( 6 )}{ln ( 60 )}

十進法表記

3.42509 \dots

解答ステップ

\frac{e ln ( 90 ) + ln ( 6 )}{ln ( 3 ) + ln ( 20 )}

対数の規則を適用する:

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

ln (3) + ln (20) = ln (3 \cdot 20)

= \frac{e ln ( 90 ) + ln ( 6 )}{ln ( 3 \cdot 20 )}

数を乗じる:

3 \cdot 20 = 60

= \frac{e ln ( 90 ) + ln ( 6 )}{ln ( 60 )}