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Popular >

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

Solution

simplify

ln (a \cdot e^{- x})

Solution

ln (a) - x

Solution steps

ln (a e^{- x})

Apply log rule:

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

ln (a e^{- x}) = ln (a) + ln (e^{- x})

= ln (a) + ln (e^{- x})

Apply log rule:

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

ln (e^{- x}) = - x ln (e)

= ln (a) - x ln (e)

x ln (e) = x

= ln (a) - x

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Frequently Asked Questions (FAQ)

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