What is (-1)/2-1/2 ln(1/2) ?

The solution to (-1)/2-1/2 ln(1/2) is -1/2+1/2 ln(2)

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simplify (-1)/2-1/2 ln(1/2)

simplify

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

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

Decimal Notation

- 0.15342 \dots

Solution steps

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

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)

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

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

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

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

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

Apply rule

- (- a) = a

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

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

ln ∣ vx ∣ - ln ∣ v ∣

ln (\frac{4}{x + 1}) + ln (x)

ln (\frac{4 + 2 2}{4 - 2 2})

- lo g_{10} (4.16 \cdot 1 0^{- 13})

What is (-1)/2-1/2 ln(1/2) ?
The solution to (-1)/2-1/2 ln(1/2) is -1/2+1/2 ln(2)