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

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

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

simplify

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

ln (3 + 22)

Decimal Notation

1.76274 \dots

Solution steps

- 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})

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

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

= ln (3 + 22)

ln (0.5 t e^{- 0.5 t})

6 lo g_{e} (x) + 4 lo g_{e} (y)

ln (5 x)

- lo g_{0.5} (2 x) - 3

ln (\frac{e ^{(x + 2)} ( 5 x + 1 ) ^{3}}{x ^{5} ( 2 x + 1 ) ^{7}})

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