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Popular >

simplify ln(x^4e^{-x})

Solution

simplify

ln (x^{4} e^{- x})

Solution

4 ln (x) - x

Solution steps

ln (x^{4} e^{- x})

Apply log rule:

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

ln (x^{4} e^{- x}) = ln (x^{4}) + ln (e^{- x})

= ln (x^{4}) + ln (e^{- x})

Apply log rule:

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

ln (x^{4}) = 4 ln (x)

= 4 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)

= 4 ln (x) - x ln (e)

x ln (e) = x

= 4 ln (x) - x

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Frequently Asked Questions (FAQ)

What is ln(x^4e^{-x}) ?
The solution to ln(x^4e^{-x}) is 4ln(x)-x