化简 ln(1/(x+h)+1)-ln(1/x+1)

解答

化简

ln (\frac{1}{x + h} + 1) - ln (\frac{1}{x} + 1)

ln (\frac{x ( 1 + x + h )}{( x + h ) ( 1 + x )})

求解步骤

ln (\frac{1}{x + h} + 1) - ln (\frac{1}{x} + 1)

使用对数计算法则:

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

ln (\frac{1}{x + h} + 1) - ln (\frac{1}{x} + 1) = ln (\frac{\frac{1}{x + h} + 1}{\frac{1}{x} + 1})

= ln (\frac{\frac{1}{x + h} + 1}{\frac{1}{x} + 1})

化简

\frac{\frac{1}{x + h} + 1}{\frac{1}{x} + 1} : \frac{x ( 1 + x + h )}{( x + h ) ( 1 + x )}

= ln (\frac{x ( 1 + x + h )}{( x + h ) ( 1 + x )})

s im pl i f y ln (1 + \frac{y ^{2}}{x ^{2}}) + ln (x)

s im pl i f y - 1.44 - 5 lo g_{10} (\frac{2.6}{10})

e x p an d lo g_{8} ((\frac{x ^{3} y}{2})^{2})

s im pl i f y - lo g_{10} (4.15 \cdot 1 0^{- 3})

s im pl i f y ln (f (6.01))