結合する (5ln(29/74))/(ln(59/74))

解

結合する

\frac{5 ln ( \frac{29}{74} )}{ln ( \frac{59}{74} )}

\frac{ln ( \frac{20511149}{7 4 ^{5}} )}{ln ( \frac{59}{74} )}

十進法表記

20.67670 \dots

解答ステップ

\frac{5 ln ( \frac{29}{74} )}{ln ( \frac{59}{74} )}

対数の規則を適用する:

a lo g_{c} (b) = lo g_{c} (b^{a})

5 ln (\frac{29}{74}) = ln ((\frac{29}{74})^{5})

= \frac{ln ( ( \frac{29}{74} ) ^{5} )}{ln ( \frac{59}{74} )}

(\frac{29}{74})^{5} = \frac{2 9 ^{5}}{7 4 ^{5}}

= \frac{ln ( \frac{2 9 ^{5}}{7 4 ^{5}} )}{ln ( \frac{59}{74} )}

2 9^{5} = 20511149

= \frac{ln ( \frac{20511149}{7 4 ^{5}} )}{ln ( \frac{59}{74} )}