簡約 (4pi10^{-7})/(2pi)ln(27/16)

解

簡約

\frac{4 \cdot π \cdot 1 0 ^{- 7}}{2 \cdot π} \cdot ln (\frac{27}{16})

\frac{1}{5000000} (3 ln (3) - 4 ln (2))

十進法表記

1.0465 E - 7

解答ステップ

\frac{4 π 1 0 ^{- 7}}{2 π} ln (\frac{27}{16})

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{27}{16}) = ln (27) - ln (16)

= \frac{1 0 ^{- 7} \cdot 4 π}{2 π} (ln (27) - ln (16))

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{4 π 1 0 ^{- 7} ( ln ( 27 ) - ln ( 16 ) )}{2 π}

共通因数を約分する:

π

= \frac{4 \cdot 1 0 ^{- 7} ( ln ( 27 ) - ln ( 16 ) )}{2}

数を割る:

\frac{4}{2} = 2

= 1 0^{- 7} \cdot 2 (ln (27) - ln (16))

ln (27) = 3 ln (3)

ln (16) = 4 ln (2)

= 1 0^{- 7} \cdot 2 (3 ln (3) - 4 ln (2))

指数の規則を適用する:

a^{- b} = \frac{1}{a ^{b}}

1 0^{- 7} = \frac{1}{1 0 ^{7}}

= 2 \cdot \frac{1}{1 0 ^{7}} (3 ln (3) - 4 ln (2))

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2}{1 0 ^{7}} (3 ln (3) - 4 ln (2))

\frac{1 \cdot 2}{1 0 ^{7}} = \frac{1}{5000000}

= \frac{1}{5000000} (3 ln (3) - 4 ln (2))