展开 ln(sqrt((x^8)/((x-3)^4)))

解答

展开

ln (\frac{x ^{8}}{( x - 3 ) ^{4}})

4 ln (x) - ln (x^{2} - 6 x + 9)

求解步骤

ln (\frac{x ^{8}}{( x - 3 ) ^{4}})

\frac{x ^{8}}{( x - 3 ) ^{4}} = \frac{x ^{4}}{x ^{2} - 6 x + 9}

= ln (\frac{x ^{4}}{x ^{2} - 6 x + 9})

使用对数计算法则:

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

ln (\frac{x ^{4}}{x ^{2} - 6 x + 9}) = ln (x^{4}) - ln (x^{2} - 6 x + 9)

= ln (x^{4}) - ln (x^{2} - 6 x + 9)

化简

ln (x^{4}) : 4 ln (x)

= 4 ln (x) - ln (x^{2} - 6 x + 9)

e x p an d \frac{( 1 - 4 ^{k + 1} )}{- 3}

e x p an d π (16 - x^{2})^{2}

e x p an d \frac{6 + 8 i}{4 + ( x + 3 ) i}

e x p an d 2 (ln (x))

e x p an d \frac{( s + 2 )}{( 5 s + 3 ) ^{\frac{3}{2}}}