簡約 (98-10ln(16)+10ln(9))/7

解

簡約

\frac{98 - 10 ln ( 16 ) + 10 ln ( 9 )}{7}

\frac{98 + 10 ln ( \frac{9}{16} )}{7}

十進法表記

13.17805 \dots

解答ステップ

\frac{98 - 10 ln ( 16 ) + 10 ln ( 9 )}{7}

対数の規則を適用する:

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

10 ln (16) = ln (1 6^{10})

= \frac{98 - ln ( 1 6 ^{10} ) + 10 ln ( 9 )}{7}

対数の規則を適用する:

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

10 ln (9) = ln (9^{10})

= \frac{98 - ln ( 1 6 ^{10} ) + ln ( 9 ^{10} )}{7}

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 (9^{10}) - ln (1 6^{10}) = ln (\frac{9 ^{10}}{1 6 ^{10}})

= \frac{98 + ln ( \frac{9 ^{10}}{1 6 ^{10}} )}{7}

ln (\frac{9 ^{10}}{1 6 ^{10}}) = 10 ln (\frac{9}{16})

= \frac{98 + 10 ln ( \frac{9}{16} )}{7}