簡約 (4ln(2))/(4ln(5)-5ln(2))

解

簡約

\frac{4 ln ( 2 )}{4 ln ( 5 ) - 5 ln ( 2 )}

\frac{4 ln ( 2 )}{ln ( \frac{625}{32} )}

十進法表記

0.93289 \dots

解答ステップ

\frac{4 ln ( 2 )}{4 ln ( 5 ) - 5 ln ( 2 )}

対数の規則を適用する:

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

4 ln (5) = ln (5^{4})

= \frac{4 ln ( 2 )}{ln ( 5 ^{4} ) - 5 ln ( 2 )}

対数の規則を適用する:

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

5 ln (2) = ln (2^{5})

= \frac{4 ln ( 2 )}{ln ( 5 ^{4} ) - ln ( 2 ^{5} )}

対数の規則を適用する:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (5^{4}) - ln (2^{5}) = ln (\frac{5 ^{4}}{2 ^{5}})

= \frac{4 ln ( 2 )}{ln ( \frac{5 ^{4}}{2 ^{5}} )}

\frac{5 ^{4}}{2 ^{5}} = \frac{625}{32}

= \frac{4 ln ( 2 )}{ln ( \frac{625}{32} )}