What is simplify-1/2+1/2 ln((4+sqrt(7))/3) ?

The solution to simplify-1/2+1/2 ln((4+sqrt(7))/3) is (-1+ln(4+sqrt(7))-ln(3))/2

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simplify-1/2+1/2 ln((4+sqrt(7))/3)

simplify

- \frac{1}{2} + \frac{1}{2} ln (\frac{4 + 7}{3})

\frac{- 1 + ln ( 4 + 7 ) - ln ( 3 )}{2}

Decimal Notation

- 0.10231 \dots

Solution steps

- \frac{1}{2} + \frac{1}{2} ln (\frac{4 + 7}{3})

Apply log rule:

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

ln (\frac{4 + 7}{3}) = ln (4 + 7) - ln (3)

= - \frac{1}{2} + \frac{1}{2} (ln (4 + 7) - ln (3))

Expand

\frac{1}{2} (ln (4 + 7) - ln (3)) : \frac{1}{2} ln (4 + 7) - \frac{1}{2} ln (3)

= - \frac{1}{2} + \frac{1}{2} ln (4 + 7) - \frac{1}{2} ln (3)

Simplify

- \frac{1}{2} + \frac{1}{2} ln (4 + 7) - \frac{1}{2} ln (3) : \frac{- 1 + ln ( 4 + 7 ) - ln ( 3 )}{2}

= \frac{- 1 + ln ( 4 + 7 ) - ln ( 3 )}{2}

- \frac{ln ( \frac{45}{203} )}{ln ( \frac{293}{313} ) - ln ( \frac{45}{203} )}

- 2 ln (a) + \frac{1}{3} ln (b) - 3 ln (c)

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

\frac{ln ( 4.1 ) - ln ( 3.9 )}{4 \cdot 0.1}

What is simplify-1/2+1/2 ln((4+sqrt(7))/3) ?
The solution to simplify-1/2+1/2 ln((4+sqrt(7))/3) is (-1+ln(4+sqrt(7))-ln(3))/2