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

The solution to 2ln((1/2-1)/(1/2+1)) is 2(ln(-1/2)-ln(3/2))

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

simplify

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

2 (ln (- \frac{1}{2}) - ln (\frac{3}{2}))

Solution steps

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

Apply log rule:

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

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

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

Join

\frac{1}{2} - 1 : - \frac{1}{2}

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

Join

\frac{1}{2} + 1 : \frac{3}{2}

= 2 (ln (- \frac{1}{2}) - ln (\frac{3}{2}))

- lo g_{10} (3.62 \cdot 1 0^{- 2})

ln (- 9 e)

ln (1.999 - 2) - ln (1.999 + 1)

2194.075 ln (- 300) - 2194.075 ln (- 1000)

ln (2 e^{3} k)

What is 2ln((1/2-1)/(1/2+1)) ?
The solution to 2ln((1/2-1)/(1/2+1)) is 2(ln(-1/2)-ln(3/2))