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Popular >

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

Solution

simplify

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

Solution

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

Solution steps

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

Apply log rule:

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

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

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

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

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

ln (4) = 2 ln (2)

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

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Frequently Asked Questions (FAQ)

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