簡約 ln((8x-2)/(sqrt(x+2))sin(e^{2x}))

解

簡約

ln (\frac{8 x - 2}{x + 2} sin (e^{2 x}))

ln (8 x - 2) - ln (x + 2) + ln (sin (e^{2 x}))

解答ステップ

ln (\frac{8 x - 2}{x + 2} sin (e^{2 x}))

対数の規則を適用する:

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

ln (\frac{8 x - 2}{x + 2} sin (e^{2 x})) = ln (\frac{8 x - 2}{x + 2}) + ln (sin (e^{2 x}))

= ln (\frac{8 x - 2}{x + 2}) + ln (sin (e^{2 x}))

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{8 x - 2}{x + 2}) = ln (8 x - 2) - ln (x + 2)

= ln (8 x - 2) - ln (x + 2) + ln (sin (e^{2 x}))