簡約 ln((d^2+3h^2)/(6h))

解

簡約

ln (\frac{d ^{2} + 3 h ^{2}}{6 h})

ln (d^{2} + 3 h^{2}) - ln (6) - ln (h)

解答ステップ

ln (\frac{d ^{2} + 3 h ^{2}}{6 h})

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{d ^{2} + 3 h ^{2}}{6 h}) = ln (d^{2} + 3 h^{2}) - ln (6 h)

= ln (d^{2} + 3 h^{2}) - ln (6 h)

対数の規則を適用する:

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

ln (6 h) = ln (6) + ln (h)

= ln (d^{2} + 3 h^{2}) - (ln (h) + ln (6))

- (ln (6) + ln (h)) : - ln (6) - ln (h)

= ln (d^{2} + 3 h^{2}) - ln (6) - ln (h)