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Popular >

simplify ln(xe^{-x})

Solution

simplify

ln (x e^{- x})

Solution

ln (x) - x

Solution steps

ln (x e^{- x})

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln (x) - x ln (e)

x ln (e) = x

= ln (x) - x

Popular Examples

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lo g_{10} (1000 x^{3} y^{5})

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simplify ln(9/2)simplify

ln (\frac{9}{2})

Frequently Asked Questions (FAQ)

What is ln(xe^{-x}) ?
The solution to ln(xe^{-x}) is ln(x)-x