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Popular >

simplify ln(1/θ e^{-x/θ})

Solution

simplify

ln (\frac{1}{θ} e^{- \frac{x}{θ}})

Solution

- \frac{x}{θ} - ln (θ)

Solution steps

ln (\frac{1}{θ} e^{- \frac{x}{θ}})

Apply log rule:

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

ln (\frac{1}{θ} e^{- \frac{x}{θ}}) = ln (\frac{1}{θ}) + ln (e^{- \frac{x}{θ}})

= ln (\frac{1}{θ}) + ln (e^{- \frac{x}{θ}})

Apply log rule:

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

ln (e^{- \frac{x}{θ}}) = - \frac{x}{θ} ln (e)

= ln (\frac{1}{θ}) - \frac{x}{θ} ln (e)

Apply log rule:

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

ln (\frac{1}{θ}) = ln (1) - ln (θ)

= ln (1) - ln (θ) - ln (e) \frac{x}{θ}

ln (1) = 0

\frac{x}{θ} ln (e) = \frac{x}{θ}

= 0 - ln (θ) - \frac{x}{θ}

0 - ln (θ) - \frac{x}{θ} = - ln (θ) - \frac{x}{θ}

= - \frac{x}{θ} - ln (θ)

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Frequently Asked Questions (FAQ)

What is ln(1/θ e^{-x/θ}) ?
The solution to ln(1/θ e^{-x/θ}) is -x/θ-ln(θ)