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Popular >

simplify ln(λe^{-λx})

Solution

simplify

ln (λ e^{- λ x})

Solution

ln (λ) - λ x

Solution steps

ln (λ e^{- λ x})

Apply log rule:

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

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

= ln (λ) + ln (e^{- λ x})

Apply log rule:

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

ln (e^{- λ x}) = - λ x ln (e)

= ln (λ) - λ x ln (e)

λ x ln (e) = λ x

= ln (λ) - λ x

Popular Examples

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1036.36 \cdot ln (\frac{576}{249.2})

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lo g_{10} (a^{2} - b^{2}) - lo g_{10} (a + b)

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2.338 - 1.4995 - 0.287 \cdot ln (\frac{675}{45})

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6 lo g_{4} (x) - 3 lo g_{4} (y)

Frequently Asked Questions (FAQ)

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