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

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

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

simplify

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

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

Decimal Notation

0.54930 \dots

Solution steps

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

Apply log rule:

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

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

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

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

= ln (3)

Rewrite as

= ln (3^{\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 (3)

ln (\frac{1.2}{0.6})

lo g_{\frac{4}{3}} (2) + lo g_{\frac{4}{3}} (8) - lo g_{\frac{4}{3}} (9)

lo g_{2} (8) - lo g_{10} (2 x) - lo g_{10} (y)

lo g_{3 x} (\frac{3}{x})

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