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Popular >

simplify ln(1/2 e^{-x})

Solution

simplify

ln (\frac{1}{2} e^{- x})

Solution

- x - ln (2)

Solution steps

ln (\frac{1}{2} e^{- x})

Apply log rule:

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

ln (\frac{1}{2} e^{- x}) = ln (\frac{1}{2}) + ln (e^{- x})

= ln (\frac{1}{2}) + ln (e^{- x})

Apply log rule:

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

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

= ln (\frac{1}{2}) - x ln (e)

Apply log rule:

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

ln (\frac{1}{2}) = ln (1) - ln (2)

= ln (1) - ln (2) - ln (e) x

ln (1) = 0

x ln (e) = x

= 0 - ln (2) - x

0 - ln (2) - x = - ln (2) - x

= - x - ln (2)

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Frequently Asked Questions (FAQ)

What is ln(1/2 e^{-x}) ?
The solution to ln(1/2 e^{-x}) is -x-ln(2)