What is ln((l^2)/(2!)e^{-l}) ?

The solution to ln((l^2)/(2!)e^{-l}) is 2ln(l)-ln(2)-l

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simplify ln((l^2)/(2!)e^{-l})

simplify

ln (\frac{l ^{2}}{2 !} e^{- l})

2 ln (l) - ln (2) - l

Solution steps

ln (\frac{l ^{2}}{2 !} e^{- l})

Apply log rule:

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

ln (\frac{l ^{2}}{2 !} e^{- l}) = ln (\frac{l ^{2}}{2 !}) + ln (e^{- l})

= ln (\frac{l ^{2}}{2 !}) + ln (e^{- l})

Apply log rule:

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

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

= ln (\frac{l ^{2}}{2 !}) - l ln (e)

Apply log rule:

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

ln (\frac{l ^{2}}{2 !}) = ln (l^{2}) - ln (2!)

= ln (l^{2}) - ln (2!) - ln (e) l

Apply log rule:

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

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

= 2 ln (l) - ln (2!) - l ln (e)

l ln (e) = l

= 2 ln (l) - ln (2!) - l

Simplify

2! : 2

= 2 ln (l) - ln (2) - l

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ln (3 (x + 2)) - \frac{ln ( x + 2 )}{2}

ln (x - 3) - 2 ln (x + 12) - ln (x)

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What is ln((l^2)/(2!)e^{-l}) ?
The solution to ln((l^2)/(2!)e^{-l}) is 2ln(l)-ln(2)-l