簡約-(2ln(2))/(ln(5)-2ln(2))

解

簡約

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

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

十進法表記

- 6.21256 \dots

解答ステップ

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

対数の規則を適用する:

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

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

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

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

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

2^{2} = 4

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