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

The solution to ln((sqrt(5))/3+1)-ln(-(sqrt(5))/3+1) is ln((7+3sqrt(5))/2)

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

simplify

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

ln (\frac{7 + 3 5}{2})

Decimal Notation

1.92484 \dots

Solution steps

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

Apply log rule:

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

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

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

\frac{\frac{5}{3} + 1}{- \frac{5}{3} + 1} = \frac{7 + 3 5}{2}

= ln (\frac{7 + 3 5}{2})

ln (7^{4}) - 2 ln (4)

ln (y + 2) + ln (y - 2)

ln (e x^{2})

ln ((θ + 1)^{n} \cdot (x^{θ}))

What is ln((sqrt(5))/3+1)-ln(-(sqrt(5))/3+1) ?
The solution to ln((sqrt(5))/3+1)-ln(-(sqrt(5))/3+1) is ln((7+3sqrt(5))/2)