What is 5ln((1-(sqrt(2))/2)/(1+(sqrt(2))/2)) ?

The solution to 5ln((1-(sqrt(2))/2)/(1+(sqrt(2))/2)) is 5(ln(1-(sqrt(2))/2)-ln(1+(sqrt(2))/2))

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simplify 5ln((1-(sqrt(2))/2)/(1+(sqrt(2))/2))

simplify

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

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

Decimal Notation

- 8.81373 \dots

Solution steps

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

Apply log rule:

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

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

= 5 (ln (- \frac{2}{2} + 1) - ln (\frac{2}{2} + 1))

\frac{1}{4} ln (15)

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

lo g_{3} (\frac{x ^{4}}{y ^{2}})

ln (2 n^{2} + 4 n - 3) - ln (n^{2} + 4 n + 5)

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

What is 5ln((1-(sqrt(2))/2)/(1+(sqrt(2))/2)) ?
The solution to 5ln((1-(sqrt(2))/2)/(1+(sqrt(2))/2)) is 5(ln(1-(sqrt(2))/2)-ln(1+(sqrt(2))/2))