展开 ln(sqrt((9x)/(x-9)))

解答

展开

ln (\frac{9 x}{x - 9})

ln (3) + \frac{1}{2} ln (x) - \frac{1}{2} ln (x - 9)

求解步骤

ln (\frac{9 x}{x - 9})

\frac{9 x}{x - 9} = \frac{3 x}{x - 9}

= ln (\frac{3 x}{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{3 x}{x - 9}) = ln (3 x) - ln (x - 9)

= ln (3 x) - ln (x - 9)

化简

ln (x - 9) : \frac{1}{2} ln (x - 9)

ln (3 x) = ln (3) + \frac{1}{2} ln (x)

= ln (3) + \frac{1}{2} ln (x) - \frac{1}{2} ln (x - 9)

e x p an d (3 x^{2} + 4 x - 5)^{5}

e x p an d \frac{( k + 1 ) ( k + 2 ) ( 2 k + 9 )}{6}

e x p an d lo g_{4} (3 x^{2} y^{4})

e x p an d - ln 1 + cos^{2} (7.5)

e x p an d \frac{8 x}{( x + 2 ) ( x - 2 )}