What is simplify-0.5ln(1/2)+1/2 ln((sqrt(3))/2) ?

The solution to simplify-0.5ln(1/2)+1/2 ln((sqrt(3))/2) is ln(1.31607…)

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simplify-0.5ln(1/2)+1/2 ln((sqrt(3))/2)

simplify

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

ln (1.31607 \dots)

Decimal Notation

0.27465 \dots

Solution steps

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

Apply log rule:

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

0.5 ln (\frac{1}{2}) = ln ((\frac{1}{2})^{0.5})

= - ln ((\frac{1}{2})^{0.5}) + \frac{1}{2} ln (\frac{3}{2})

Apply log rule:

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

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

= - ln ((\frac{1}{2})^{0.5}) + ln (\frac{3}{2})^{\frac{1}{2}}

Apply log rule:

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

ln (\frac{3}{2})^{\frac{1}{2}} - ln ((\frac{1}{2})^{0.5}) = ln \frac{( \frac{3}{2} ) ^{\frac{1}{2}}}{( \frac{1}{2} ) ^{0.5}}

= ln \frac{( \frac{3}{2} ) ^{\frac{1}{2}}}{( \frac{1}{2} ) ^{0.5}}

\frac{( \frac{3}{2} ) ^{\frac{1}{2}}}{( \frac{1}{2} ) ^{0.5}} = 1.31607 \dots

= ln (1.31607 \dots)

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What is simplify-0.5ln(1/2)+1/2 ln((sqrt(3))/2) ?
The solution to simplify-0.5ln(1/2)+1/2 ln((sqrt(3))/2) is ln(1.31607…)