What is ln(-4x^2e^{-x^2}) ?

The solution to ln(-4x^2e^{-x^2}) is 2ln(2)+2ln(x)-x^2

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simplify ln(-4x^2e^{-x^2})

simplify

ln (- 4 x^{2} e^{- x^{2}})

2 ln (2) + 2 ln (x) - x^{2}

Solution steps

ln (- 4 x^{2} e^{- x^{2}})

Apply log rule:

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

ln (- 4 x^{2} e^{- x^{2}}) = ln (4) + ln (x^{2}) + ln (e^{- x^{2}})

= ln (4) + ln (x^{2}) + ln (e^{- x^{2}})

Apply log rule:

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

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

= ln (4) + 2 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)

= ln (4) + 2 ln (x) - x^{2} ln (e)

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

= ln (4) + 2 ln (x) - x^{2}

ln (4) = 2 ln (2)

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

ln (\frac{236409}{388533}) - ln (1 - \frac{236409}{388533})

ln (\frac{2 ^{4}}{3 ^{2} 5 ^{- 4}})

ln (8 x) - ln (2 x)

ln (\frac{1}{( r - 1 ) !} θ^{- w} x^{w - 1} e^{- x θ^{- 1}})

What is ln(-4x^2e^{-x^2}) ?
The solution to ln(-4x^2e^{-x^2}) is 2ln(2)+2ln(x)-x^2