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Popular >

simplify log_{e}(ke^{-ax})

Solution

simplify

lo g_{e} (k \cdot e^{- a \cdot x})

Solution

ln (k) - a x

Solution steps

lo g_{e} (k e^{- a x})

Apply log rule:

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

lo g_{e} (k e^{- a x}) = lo g_{e} (k) + lo g_{e} (e^{- a x})

= lo g_{e} (k) + lo g_{e} (e^{- a x})

Apply log rule:

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

lo g_{e} (e^{- a x}) = - a x lo g_{e} (e)

= lo g_{e} (k) - a x lo g_{e} (e)

lo g_{e} (k) = ln (k)

a x lo g_{e} (e) = a x

= ln (k) - a x

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Frequently Asked Questions (FAQ)

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