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Popular >

simplify ln(1/β e^{-x/β})

Solution

simplify

ln (\frac{1}{β} e^{- \frac{x}{β}})

Solution

- \frac{x}{β} - ln (β)

Solution steps

ln (\frac{1}{β} e^{- \frac{x}{β}})

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (\frac{1}{β}) = ln (1) - ln (β)

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

ln (1) = 0

\frac{x}{β} ln (e) = \frac{x}{β}

= 0 - ln (β) - \frac{x}{β}

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

= - \frac{x}{β} - ln (β)

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Frequently Asked Questions (FAQ)

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