What is ln(-0.00004e^{(-0.00228t)}) ?

The solution to ln(-0.00004e^{(-0.00228t)}) is ln(0.00004)-0.00228t

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simplify ln(-0.00004e^{(-0.00228t)})

simplify

ln (- 0.00004 e^{(- 0.00228 t)})

ln (0.00004) - 0.00228 t

Solution steps

ln (- 0.00004 e^{(- 0.00228 t)})

Apply log rule:

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

ln (- 0.00004 e^{(- 0.00228 t)}) = ln (0.00004) + ln (e^{(- 0.00228 t)})

= ln (0.00004) + ln (e^{(- 0.00228 t)})

Apply log rule:

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

ln (e^{(- 0.00228 t)}) = (- 0.00228 t) ln (e)

= ln (0.00004) + (- 0.00228 t) ln (e)

Remove parentheses:

(- a) = - a

= ln (0.00004) - 0.00228 t ln (e)

0.00228 t ln (e) = 0.00228 t

= ln (0.00004) - 0.00228 t

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What is ln(-0.00004e^{(-0.00228t)}) ?
The solution to ln(-0.00004e^{(-0.00228t)}) is ln(0.00004)-0.00228t