What is 1/2 ln(8)-1/2 ln(3) ?

The solution to 1/2 ln(8)-1/2 ln(3) is ln((2sqrt(6))/3)

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simplify 1/2 ln(8)-1/2 ln(3)

simplify

\frac{1}{2} ln (8) - \frac{1}{2} ln (3)

ln (\frac{2 6}{3})

Decimal Notation

0.49041 \dots

Solution steps

\frac{1}{2} ln (8) - \frac{1}{2} ln (3)

Apply log rule:

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

\frac{1}{2} ln (8) = ln (8^{\frac{1}{2}})

= ln (8^{\frac{1}{2}}) - \frac{1}{2} ln (3)

Apply log rule:

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

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

= ln (8^{\frac{1}{2}}) - ln (3^{\frac{1}{2}})

Apply log rule:

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

ln (8^{\frac{1}{2}}) - ln (3^{\frac{1}{2}}) = ln (\frac{8 ^{\frac{1}{2}}}{3 ^{\frac{1}{2}}})

= ln (\frac{8 ^{\frac{1}{2}}}{3 ^{\frac{1}{2}}})

\frac{8 ^{\frac{1}{2}}}{3 ^{\frac{1}{2}}} = \frac{2 6}{3}

= ln (\frac{2 6}{3})

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What is 1/2 ln(8)-1/2 ln(3) ?
The solution to 1/2 ln(8)-1/2 ln(3) is ln((2sqrt(6))/3)