What is ln(Ae^{(-e/(RT))}) ?

The solution to ln(Ae^{(-e/(RT))}) is ln(A)-e/(RT)

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simplify ln(Ae^{(-e/(RT))})

simplify

ln (A e^{(- \frac{e}{RT})})

ln (A) - \frac{e}{RT}

Solution steps

ln (A e^{(- \frac{e}{RT})})

Apply log rule:

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

ln (A e^{(- \frac{e}{RT})}) = ln (A) + ln (e^{(- \frac{e}{RT})})

= ln (A) + ln (e^{(- \frac{e}{RT})})

Apply log rule:

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

ln (e^{(- \frac{e}{RT})}) = (- \frac{e}{RT}) ln (e)

= ln (A) + (- \frac{e}{RT}) ln (e)

Remove parentheses:

(- a) = - a

= ln (A) - \frac{e}{RT} ln (e)

\frac{e}{RT} ln (e) = \frac{e}{RT}

= ln (A) - \frac{e}{RT}

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