What is simplify-ln(1-e^λ)-ln(y!) ?

The solution to simplify-ln(1-e^λ)-ln(y!) is -ln((1-e^λ)y!)

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simplify-ln(1-e^λ)-ln(y!)

simplify

- ln (1 - e^{λ}) - ln (y!)

- ln ((1 - e^{λ}) y!)

Solution steps

- ln (1 - e^{λ}) - ln (y!)

Rewrite

- ln (- e^{λ} + 1) - ln (y!)

- (ln (- e^{λ} + 1) + ln (y!))

= - (ln (y!) + ln (- e^{λ} + 1))

Apply log rule:

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

ln (1 - e^{λ}) + ln (y!) = ln (y! (- e^{λ} + 1))

= - ln ((1 - e^{λ}) y!)

ln (a^{n} \cdot e^{- a \cdot (x - b)})

lo g_{7} (x) + \frac{1}{2} lo g_{7} (y^{6}) - 2 lo g_{7} (z)

30 \cdot ln (\frac{3}{0.2})

lo g_{10} (\frac{z ^{3}}{x ^{2} y ^{5}})

0.0259 \cdot ln (\frac{( 4.7 \cdot 1 0 ^{17} )}{1.2 \cdot 1 0 ^{18}})

What is simplify-ln(1-e^λ)-ln(y!) ?
The solution to simplify-ln(1-e^λ)-ln(y!) is -ln((1-e^λ)y!)