簡約 1/2 (ln(3^2)-ln(5^4)-ln(2^2))

解

簡約

\frac{1}{2} (ln (3^{2}) - ln (5^{4}) - ln (2^{2}))

\frac{1}{2} ln (\frac{9}{2500})

十進法表記

- 2.81341 \dots

解答ステップ

\frac{1}{2} (ln (3^{2}) - ln (5^{4}) - 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 (3^{2}) - ln (5^{4}) = ln (\frac{3 ^{2}}{5 ^{4}})

= \frac{1}{2} (ln (\frac{3 ^{2}}{5 ^{4}}) - ln (2^{2}))

\frac{3 ^{2}}{5 ^{4}} = \frac{9}{625}

= \frac{1}{2} (ln (\frac{9}{625}) - 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 (\frac{9}{625}) - ln (2^{2}) = ln (\frac{\frac{9}{625}}{2 ^{2}})

= \frac{1}{2} ln (\frac{\frac{9}{625}}{2 ^{2}})

\frac{\frac{9}{625}}{2 ^{2}} = \frac{9}{2500}

= \frac{1}{2} ln (\frac{9}{2500})