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

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

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

simplify

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

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

Decimal Notation

0.20273 \dots

Solution steps

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

Apply log rule:

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

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

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

\frac{\frac{3}{2}}{\frac{2}{2}} = \frac{3}{2}

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

Rewrite as

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

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

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

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