What is join 1/3 ln(2+sqrt(3)) ?

The solution to join 1/3 ln(2+sqrt(3)) is ln((2+sqrt(3))^{1/3})

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join 1/3 ln(2+sqrt(3))

join

\frac{1}{3} ln (2 + 3)

ln ((2 + 3)^{\frac{1}{3}})

Decimal Notation

0.43898 \dots

Solution steps

\frac{1}{3} ln (2 + 3)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{3} ln (2 + 3) = ln ((2 + 3)^{\frac{1}{3}})

= ln ((2 + 3)^{\frac{1}{3}})

- 2 ln (\frac{3}{4}) - ln (6)

3 (lo g_{6} (x) + 2 lo g_{6} (y) - 3 lo g_{6} (z))

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0.04 + 0.36 lo g_{10} (2) + 0.57 lo g_{10} (5)

What is join 1/3 ln(2+sqrt(3)) ?
The solution to join 1/3 ln(2+sqrt(3)) is ln((2+sqrt(3))^{1/3})