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

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

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

simplify

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

2 ln (3 + 22)

Decimal Notation

3.52549 \dots

Solution steps

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

Apply log rule:

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

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

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

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

= 2 ln (3 + 22)

lo g_{30} (15 0^{\circ})

ln (\frac{0.0136446}{0.00350107})

lo g_{4} (x^{4}) \cdot y

ln (x^{15} \frac{y ^{19}}{z ^{12}})

ln (\frac{e ^{7}}{11})

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