簡約 ln(9/(7^4sqrt(8)))

解

簡約

ln (\frac{9}{7 ^{4} 8})

2 ln (3) - 4 ln (7) - \frac{3}{2} ln (2)

十進法表記

- 6.62613 \dots

解答ステップ

ln (\frac{9}{7 ^{4} 8})

対数の規則を適用する:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{9}{7 ^{4} 8}) = ln (9) - ln (7^{4} 8)

= ln (9) - ln (7^{4} 8)

対数の規則を適用する:

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

ln (7^{4} 8) = ln (7^{4}) + ln (8)

= ln (9) - (ln (7^{4}) + ln (8))

対数の規則を適用する:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (7^{4}) = 4 ln (7)

= ln (9) - (4 ln (7) + ln (8))

ln (8) = \frac{3}{2} ln (2)

= ln (9) - (4 ln (7) + \frac{3}{2} ln (2))

ln (9) = 2 ln (3)

= 2 ln (3) - (4 ln (7) + \frac{3}{2} ln (2))

= 2 ln (3) - (4 ln (7) + \frac{3}{2} ln (2))

- (4 ln (7) + ln (2) \frac{3}{2}) : - 4 ln (7) - ln (2) \frac{3}{2}

= 2 ln (3) - 4 ln (7) - ln (2) \frac{3}{2}

= 2 ln (3) - 4 ln (7) - \frac{3}{2} ln (2)