簡約 ((0+5)/4)^2*ln((0+5)/4)

解

簡約

(\frac{0 + 5}{4})^{2} \cdot ln (\frac{0 + 5}{4})

\frac{25}{16} (ln (5) - 2 ln (2))

十進法表記

0.34866 \dots

解答ステップ

(\frac{0 + 5}{4})^{2} ln (\frac{0 + 5}{4})

対数の規則を適用する:

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

ln (\frac{0 + 5}{4}) = ln (0 + 5) - ln (4)

= (\frac{0 + 5}{4})^{2} (ln (0 + 5) - ln (4))

(\frac{0 + 5}{4})^{2} = \frac{5 ^{2}}{4 ^{2}}

= \frac{5 ^{2}}{4 ^{2}} (ln (0 + 5) - ln (4))

数を足す:

0 + 5 = 5

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

\frac{5 ^{2}}{4 ^{2}} = \frac{25}{16}

= \frac{25}{16} (ln (5) - ln (4))

ln (4) = 2 ln (2)

= \frac{25}{16} (ln (5) - 2 ln (2))