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Popular >

simplify ln(θ^{-1}e^{-x/θ})

Solution

simplify

ln (θ^{- 1} e^{- \frac{x}{θ}})

Solution

- ln (θ) - \frac{x}{θ}

Solution steps

ln (θ^{- 1} e^{- \frac{x}{θ}})

Apply log rule:

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

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

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

Apply log rule:

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

ln (θ^{- 1}) = - 1 \cdot ln (θ)

= - 1 \cdot ln (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)

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

1 \cdot ln (θ) = ln (θ)

\frac{x}{θ} ln (e) = \frac{x}{θ}

= - ln (θ) - \frac{x}{θ}

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Frequently Asked Questions (FAQ)

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