簡約 ln(1/m e^{(-(x-2))/m})

解

簡約

ln (\frac{1}{m} e^{\frac{- ( x - 2 )}{m}})

- \frac{x - 2}{m} - ln (m)

解答ステップ

ln (\frac{1}{m} e^{\frac{- ( x - 2 )}{m}})

対数の規則を適用する:

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

ln (\frac{1}{m} e^{\frac{- ( x - 2 )}{m}}) = ln (\frac{1}{m}) + ln (e^{\frac{- ( x - 2 )}{m}})

= ln (\frac{1}{m}) + ln (e^{\frac{- ( x - 2 )}{m}})

対数の規則を適用する:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (e^{\frac{- ( x - 2 )}{m}}) = \frac{- ( x - 2 )}{m} ln (e)

= ln (\frac{1}{m}) + \frac{- ( x - 2 )}{m} ln (e)

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{1}{m}) = ln (1) - ln (m)

= ln (1) - ln (m) + ln (e) \frac{- ( x - 2 )}{m}

ln (1) = 0

\frac{- ( x - 2 )}{m} ln (e) = - \frac{x - 2}{m}

= 0 - ln (m) - \frac{x - 2}{m}

0 - ln (m) - \frac{x - 2}{m} = - ln (m) - \frac{x - 2}{m}

= - \frac{x - 2}{m} - ln (m)