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

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

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

simplify

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

\frac{1}{2} ln (3 + 22)

Decimal

0.88137 \dots

Solution steps

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

Apply log rule:

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

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

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

\frac{1 + 2}{- 1 + 2} = 3 + 22

= \frac{1}{2} ln (3 + 22)

2 ln (6) - 3 ln (x)

ln (\frac{a ^{2}}{b ^{- 1} c ^{1}})

\frac{2}{3} \cdot lo g_{10} (7.71 \cdot 1 0^{28}) - 9.1

- lo g_{10} (8.7 \cdot 1 0^{- 12})

ln (0.61022 \cdot 1 0^{- 5})

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