What is 2ln((20+sqrt(409))/3) ?

The solution to 2ln((20+sqrt(409))/3) is 2(ln(20+sqrt(409))-ln(3))

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simplify 2ln((20+sqrt(409))/3)

simplify

2 ln (\frac{20 + 409}{3})

2 (ln (20 + 409) - ln (3))

Decimal Notation

5.19169 \dots

Solution steps

2 ln (\frac{20 + 409}{3})

Apply log rule:

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

ln (\frac{20 + 409}{3}) = ln (20 + 409) - ln (3)

= 2 (ln (20 + 409) - ln (3))

2 ln (2 + 1)

ln (\frac{11}{13})

lo g_{10} (\frac{3 x ^{3}}{y})

ln^{3} (\frac{1}{x})

- lo g_{10} (5.8 \cdot 1 0^{- 9})

What is 2ln((20+sqrt(409))/3) ?
The solution to 2ln((20+sqrt(409))/3) is 2(ln(20+sqrt(409))-ln(3))