What is ln((x^{3.9644}e^{-x})/(3.9644!)) ?

The solution to ln((x^{3.9644}e^{-x})/(3.9644!)) is 3.9644ln(x)-x-ln(3.9644!)

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simplify ln((x^{3.9644}e^{-x})/(3.9644!))

simplify

ln (\frac{x ^{3.9644} e ^{- x}}{3.9644 !})

3.9644 ln (x) - x - ln (3.9644!)

Solution steps

ln (\frac{x ^{3.9644} e ^{- x}}{3.9644 !})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{x ^{3.9644} e ^{- x}}{3.9644 !}) = ln (x^{3.9644} e^{- x}) - ln (3.9644!)

= ln (e^{- x} x^{3.9644}) - ln (3.9644!)

Apply log rule:

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

ln (x^{3.9644} e^{- x}) = ln (x^{3.9644}) + ln (e^{- x})

= ln (x^{3.9644}) + ln (e^{- x}) - ln (3.9644!)

Apply log rule:

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

ln (x^{3.9644}) = 3.9644 ln (x)

= 3.9644 ln (x) + ln (e^{- x}) - ln (3.9644!)

Apply log rule:

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

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

= 3.9644 ln (x) - x ln (e) - ln (3.9644!)

x ln (e) = x

= 3.9644 ln (x) - x - ln (3.9644!)

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What is ln((x^{3.9644}e^{-x})/(3.9644!)) ?
The solution to ln((x^{3.9644}e^{-x})/(3.9644!)) is 3.9644ln(x)-x-ln(3.9644!)