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

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

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

simplify

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

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

Decimal

0.32080 \dots

Solution steps

\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} (ln (3 + 5) - ln (2))

∣ 4 ln (2) - 1 ∣ + ∣ 4 ln (3) - 3 - 4 ln (2) ∣

\frac{2 ln ( \frac{55}{9} )}{ln ( 2 )}

lo g_{10} (\frac{x z ^{2}}{y})

ln (x + 3) - ln (4)

2 ln (10) - ln (5) - 2 ln (2) + ln (3)

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