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

The solution to simplify-1/2 ln(3)+ln(1/2)-1 is ln((sqrt(3))/6)-1

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

simplify

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

ln (\frac{3}{6}) - 1

Decimal Notation

- 2.24245 \dots

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

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

\frac{\frac{1}{2}}{3 ^{\frac{1}{2}}} = \frac{3}{6}

= ln (\frac{3}{6}) - 1

ln (\frac{( x + 1 ^{2} )}{( x - 1 ^{4} )})

ln (\frac{ab}{c d})

1 ln (\frac{68}{75})

ln (e^{2} - e^{4} - 1) - ln (2 - 5)

ln (\frac{5.6}{0.25} \cdot 1 0^{- 7})

What is simplify-1/2 ln(3)+ln(1/2)-1 ?
The solution to simplify-1/2 ln(3)+ln(1/2)-1 is ln((sqrt(3))/6)-1