簡約 e^{3/2 (ln(90000)-5/3 ln(10000))}

解

簡約

e^{\frac{3}{2} (l n (90000) - \frac{5}{3} l n (10000))}

e^{\frac{3 l n ( \frac{9 3 10}{1000} )}{2}}

十進法表記

0.0027

解答ステップ

e^{\frac{3}{2} (l n (90000) - \frac{5}{3} l n (10000))}

対数の規則を適用する:

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

\frac{5}{3} ln (10000) = ln (1000 0^{\frac{5}{3}})

= e^{\frac{3}{2} (l n (90000) - l n (1000 0^{\frac{5}{3}}))}

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 (90000) - ln (1000 0^{\frac{5}{3}}) = ln (\frac{90000}{1000 0 ^{\frac{5}{3}}})

= e^{\frac{3}{2} l n (\frac{90000}{1000 0 ^{\frac{5}{3}}})}

\frac{90000}{1000 0 ^{\frac{5}{3}}} = \frac{9 3 10}{1000}

= e^{\frac{3}{2} l n (\frac{9 3 10}{1000})}

乗じる

\frac{3}{2} ln (\frac{9 3 10}{1000}) : \frac{3 ln ( \frac{9}{100 \cdot 1 0 ^{\frac{2}{3}}} )}{2}

= e^{\frac{3 l n ( \frac{9}{100 \cdot 1 0 ^{\frac{2}{3}}} )}{2}}

\frac{3 ln ( \frac{9}{100 \cdot 1 0 ^{\frac{2}{3}}} )}{2} = \frac{3 ln ( \frac{9 3 10}{1000} )}{2}

= e^{\frac{3 l n ( \frac{9 3 10}{1000} )}{2}}