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Popular >

simplify ln(2λe^{(-2λ)})

Solution

simplify

ln (2 λ e^{(- 2 λ)})

Solution

ln (2) + ln (λ) - 2 λ

Solution steps

ln (2 λ e^{(- 2 λ)})

Apply log rule:

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

ln (2 λ e^{(- 2 λ)}) = ln (2) + ln (λ) + ln (e^{(- 2 λ)})

= ln (2) + ln (λ) + ln (e^{(- 2 λ)})

Apply log rule:

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

ln (e^{(- 2 λ)}) = (- 2 λ) ln (e)

= ln (2) + ln (λ) + (- 2 λ) ln (e)

Remove parentheses:

(- a) = - a

= ln (2) + ln (λ) - 2 λ ln (e)

2 λ ln (e) = 2 λ

= ln (2) + ln (λ) - 2 λ

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Frequently Asked Questions (FAQ)

What is ln(2λe^{(-2λ)}) ?
The solution to ln(2λe^{(-2λ)}) is ln(2)+ln(λ)-2λ