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

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

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

simplify

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

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

Decimal Notation

1.76274 \dots

Solution steps

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

Apply log rule:

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

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

= ln (1 + 2) - ln (2 - 1)

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

- \frac{4}{6} lo g_{2} (\frac{4}{6}) - \frac{2}{6} lo g_{2} (\frac{2}{6})

lo g_{5} (6) + lo g_{5} (11)

lo g_{3} (\frac{27}{y})

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

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