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Popular >

simplify ln(ae^{-bt})

Solution

simplify

ln (a e^{- b t})

Solution

ln (a) - b t

Solution steps

ln (a e^{- b t})

Apply log rule:

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

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

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

Apply log rule:

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

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

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

b t ln (e) = b t

= ln (a) - b t

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Frequently Asked Questions (FAQ)

What is ln(ae^{-bt}) ?
The solution to ln(ae^{-bt}) is ln(a)-bt