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Popular >

simplify ln(x^3e^{-x^2})

Solution

simplify

ln (x^{3} e^{- x^{2}})

Solution

3 ln (x) - x^{2}

Solution steps

ln (x^{3} e^{- x^{2}})

Apply log rule:

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

ln (x^{3} e^{- x^{2}}) = ln (x^{3}) + ln (e^{- x^{2}})

= ln (x^{3}) + ln (e^{- x^{2}})

Apply log rule:

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

ln (x^{3}) = 3 ln (x)

= 3 ln (x) + ln (e^{- x^{2}})

Apply log rule:

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

ln (e^{- x^{2}}) = - x^{2} ln (e)

= 3 ln (x) - x^{2} ln (e)

x^{2} ln (e) = x^{2}

= 3 ln (x) - x^{2}

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Frequently Asked Questions (FAQ)

What is ln(x^3e^{-x^2}) ?
The solution to ln(x^3e^{-x^2}) is 3ln(x)-x^2