簡約-(2ln(10)+ln(97))/6

解

簡約

- \frac{2 ln ( 10 ) + ln ( 97 )}{6}

- \frac{ln ( 9700 )}{6}

十進法表記

- 1.52998 \dots

解答ステップ

- \frac{2 ln ( 10 ) + ln ( 97 )}{6}

対数の規則を適用する:

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

2 ln (10) = ln (1 0^{2})

= - \frac{ln ( 97 ) + ln ( 1 0 ^{2} )}{6}

対数の規則を適用する:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (1 0^{2}) + ln (97) = ln (1 0^{2} \cdot 97)

= - \frac{ln ( 1 0 ^{2} \cdot 97 )}{6}

1 0^{2} \cdot 97 = 9700

= - \frac{ln ( 9700 )}{6}