結合する (38ln(9/10))/(ln(2))

解

結合する

\frac{38 ln ( \frac{9}{10} )}{ln ( 2 )}

\frac{ln ( \frac{9 ^{38}}{1 0 ^{38}} )}{ln ( 2 )}

十進法表記

- 5.77611 \dots

解答ステップ

\frac{38 ln ( \frac{9}{10} )}{ln ( 2 )}

対数の規則を適用する:

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

38 ln (\frac{9}{10}) = ln ((\frac{9}{10})^{38})

= \frac{ln ( ( \frac{9}{10} ) ^{38} )}{ln ( 2 )}

(\frac{9}{10})^{38} = \frac{9 ^{38}}{1 0 ^{38}}

= \frac{ln ( \frac{9 ^{38}}{1 0 ^{38}} )}{ln ( 2 )}