結合する (ln(9/1024))/(2ln(243/16))

解

結合する

\frac{ln ( \frac{9}{1024} )}{2 ln ( \frac{243}{16} )}

\frac{ln ( \frac{9}{1024} )}{ln ( \frac{59049}{256} )}

十進法表記

- 0.87011 \dots

解答ステップ

\frac{ln ( \frac{9}{1024} )}{2 ln ( \frac{243}{16} )}

対数の規則を適用する:

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

2 ln (\frac{243}{16}) = ln ((\frac{243}{16})^{2})

= \frac{ln ( \frac{9}{1024} )}{ln ( ( \frac{243}{16} ) ^{2} )}

(\frac{243}{16})^{2} = \frac{24 3 ^{2}}{1 6 ^{2}}

= \frac{ln ( \frac{9}{1024} )}{ln ( \frac{24 3 ^{2}}{1 6 ^{2}} )}

\frac{24 3 ^{2}}{1 6 ^{2}} = \frac{59049}{256}

= \frac{ln ( \frac{9}{1024} )}{ln ( \frac{59049}{256} )}