化简 ln(c)-ln(d)+ln(0.017+c)-ln(0.017-d)

解答

化简

ln (c) - ln (d) + ln (0.017 + c) - ln (0.017 - d)

ln (\frac{c ( 0.017 + c )}{d ( 0.017 - d )})

求解步骤

ln (c) - ln (d) + ln (0.017 + c) - ln (0.017 - d)

使用对数计算法则:

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

ln (c) - ln (d) = ln (\frac{c}{d})

= ln (\frac{c}{d}) + ln (0.017 + c) - ln (0.017 - d)

使用对数计算法则:

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

ln (\frac{c}{d}) + ln (0.017 + c) = ln (\frac{c}{d} (c + 0.017))

= ln (\frac{c}{d} (c + 0.017)) - ln (- d + 0.017)

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= ln (\frac{c ( 0.017 + c )}{d}) - ln (0.017 - d)

使用对数计算法则:

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

ln (\frac{c ( 0.017 + c )}{d}) - ln (0.017 - d) = ln (\frac{\frac{c ( c + 0.017 )}{d}}{- d + 0.017})

= ln (\frac{\frac{c ( 0.017 + c )}{d}}{0.017 - d})

使用分式法则:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= ln (\frac{c ( 0.017 + c )}{d ( 0.017 - d )})

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