結合する (2ln(55/9))/(ln(2))

解

結合する

\frac{2 ln ( \frac{55}{9} )}{ln ( 2 )}

\frac{ln ( \frac{3025}{81} )}{ln ( 2 )}

十進法表記

5.22286 \dots

解答ステップ

\frac{2 ln ( \frac{55}{9} )}{ln ( 2 )}

対数の規則を適用する:

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

2 ln (\frac{55}{9}) = ln ((\frac{55}{9})^{2})

= \frac{ln ( ( \frac{55}{9} ) ^{2} )}{ln ( 2 )}

(\frac{55}{9})^{2} = \frac{5 5 ^{2}}{9 ^{2}}

= \frac{ln ( \frac{5 5 ^{2}}{9 ^{2}} )}{ln ( 2 )}

\frac{5 5 ^{2}}{9 ^{2}} = \frac{3025}{81}

= \frac{ln ( \frac{3025}{81} )}{ln ( 2 )}