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

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

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

simplify

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

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

Decimal Notation

0.14384 \dots

Solution steps

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

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 (2)

Apply log rule:

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

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

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

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

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

- \frac{29886}{ln ( 10 ) 35}

ln (\frac{4}{x}) + ln (\frac{2}{x ^{3}})

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

ln (\frac{2}{2.8})

7 lo g_{5} (a) + 4 lo g_{5} (z)

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