簡約 1/5 (6ln(5)-ln(2))

解

簡約

\frac{1}{5} (6 ln (5) - ln (2))

\frac{1}{5} ln (\frac{15625}{2})

十進法表記

1.79269 \dots

解答ステップ

\frac{1}{5} (6 ln (5) - ln (2))

対数の規則を適用する:

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

6 ln (5) = ln (5^{6})

= \frac{1}{5} (ln (5^{6}) - ln (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^{6}) - ln (2) = ln (\frac{5 ^{6}}{2})

= \frac{1}{5} ln (\frac{5 ^{6}}{2})

5^{6} = 15625

= \frac{1}{5} ln (\frac{15625}{2})