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Popular >

simplify ln(θ*e^{-θx})

Solution

simplify

ln (θ \cdot e^{- θ x})

Solution

ln (θ) - θ x

Solution steps

ln (θ e^{- θ x})

Apply log rule:

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

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

= ln (θ) + ln (e^{- θ x})

Apply log rule:

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

ln (e^{- θ x}) = - θ x ln (e)

= ln (θ) - θ x ln (e)

θ x ln (e) = θ x

= ln (θ) - θ x

Popular Examples

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lo g_{5} (5 e^{10} \cdot 125)

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ln (x + 2) - ln (x^{2} + 2 x)

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(2.5 \cdot ln (2) + ln (3)) \cdot 0.831

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2000 (ln (140000) - ln (87500)) - 245

Frequently Asked Questions (FAQ)

What is ln(θ*e^{-θx}) ?
The solution to ln(θ*e^{-θx}) is ln(θ)-θx