What is simplify-1/3+1/3 ln((3+sqrt(5))/2) ?

The solution to simplify-1/3+1/3 ln((3+sqrt(5))/2) is (-1+ln(3+sqrt(5))-ln(2))/3

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simplify-1/3+1/3 ln((3+sqrt(5))/2)

simplify

- \frac{1}{3} + \frac{1}{3} ln (\frac{3 + 5}{2})

\frac{- 1 + ln ( 3 + 5 ) - ln ( 2 )}{3}

Decimal Notation

- 0.01252 \dots

Solution steps

- \frac{1}{3} + \frac{1}{3} ln (\frac{3 + 5}{2})

Apply log rule:

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

ln (\frac{3 + 5}{2}) = ln (3 + 5) - ln (2)

= - \frac{1}{3} + \frac{1}{3} (ln (3 + 5) - ln (2))

Expand

\frac{1}{3} (ln (3 + 5) - ln (2)) : \frac{1}{3} ln (3 + 5) - \frac{1}{3} ln (2)

= - \frac{1}{3} + \frac{1}{3} ln (3 + 5) - \frac{1}{3} ln (2)

Simplify

- \frac{1}{3} + \frac{1}{3} ln (3 + 5) - \frac{1}{3} ln (2) : \frac{- 1 + ln ( 3 + 5 ) - ln ( 2 )}{3}

= \frac{- 1 + ln ( 3 + 5 ) - ln ( 2 )}{3}

3 ln (2) - 2 ln (3)

\frac{6 ln ( 3 ) - 10 ln ( 2 )}{2}

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

ln (\frac{7 x ^{5}}{y ^{3}})

ln (9616) - 2 ln (96)

What is simplify-1/3+1/3 ln((3+sqrt(5))/2) ?
The solution to simplify-1/3+1/3 ln((3+sqrt(5))/2) is (-1+ln(3+sqrt(5))-ln(2))/3