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

The solution to 1/2 ln((sqrt(3))/4)-1/2 ln(1/2) is ln((\sqrt[4]{3}sqrt(2))/2)

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

simplify

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

Decimal Notation

- 0.07192 \dots

Solution steps

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

Apply log rule:

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

\frac{1}{2} ln (\frac{3}{4}) = ln (\frac{3}{4})^{\frac{1}{2}}

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln \frac{( \frac{3}{4} ) ^{\frac{1}{2}}}{( \frac{1}{2} ) ^{\frac{1}{2}}}

\frac{1}{3} lo g_{2} (3)

5 lo g_{5} (7 y + 1) + \frac{1}{2} lo g_{5} (y + 5)

ln (\frac{2 x}{a ^{2}})

6 lo g_{5} (z - 4) - 3 lo g_{5} (z + 5)

lo g_{10} (\frac{10}{x ( x ^{2} + 1 ) ( x ^{4} + 2 )})

What is 1/2 ln((sqrt(3))/4)-1/2 ln(1/2) ?
The solution to 1/2 ln((sqrt(3))/4)-1/2 ln(1/2) is ln((\sqrt[4]{3}sqrt(2))/2)