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

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

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

simplify

22 + ln (1 + 2) - ln (- 1 + 2)

22 + ln (3 + 22)

Decimal Notation

4.59117 \dots

Solution steps

22 + 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})

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

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

= 22 + ln (3 + 22)

- lo g_{10} (0.8 \cdot 1 0^{- 2})

4 (lo g_{3} (y) - 5 lo g_{3} (x)) + 2 lo g_{3} (z)

ln (\frac{2 e ^{y}}{( y + 1 )})

lo g_{10} (31.6) + 3 lo g_{10} (8 (5)) - 2.92

ln (\frac{1.26}{2 \cdot 0.085})

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