What is ln((2*sqrt(3))/3) ?

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

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simplify ln((2*sqrt(3))/3)

simplify

ln (\frac{2 \cdot 3}{3})

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

Solution steps

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

Apply log rule:

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

ln (\frac{2 3}{3}) = ln (23) - ln (3)

= ln (23) - ln (3)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (23) = ln (2) + ln (3)

= ln (2) + ln (3) - ln (3)

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

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

Add similar elements:

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

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

ln (\frac{51.104}{47.2})

ln (- 1 (1))

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

ln (ln (x)) - ln (s)

ln (x^{- 1}) - ln (x^{2})

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