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Popular >

simplify ln(a*e^{(-kt)})

Solution

simplify

ln (a \cdot e^{(- k t)})

Solution

ln (a) - k t

Solution steps

ln (a e^{(- k t)})

Apply log rule:

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

ln (a e^{(- k t)}) = ln (a) + ln (e^{(- k t)})

= ln (a) + ln (e^{(- k t)})

Apply log rule:

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

ln (e^{(- k t)}) = (- k t) ln (e)

= ln (a) + (- k t) ln (e)

Remove parentheses:

(- a) = - a

= ln (a) - k t ln (e)

k t ln (e) = k t

= ln (a) - k t

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Frequently Asked Questions (FAQ)

What is ln(a*e^{(-kt)}) ?
The solution to ln(a*e^{(-kt)}) is ln(a)-kt