What is ln(pi/4)*sqrt(pi/4) ?

The solution to ln(pi/4)*sqrt(pi/4) is (sqrt(pi))/2 ln(pi)-sqrt(pi)ln(2)

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simplify ln(pi/4)*sqrt(pi/4)

simplify

ln (\frac{π}{4}) \cdot \frac{π}{4}

\frac{π}{2} ln (π) - π ln (2)

Decimal Notation

- 0.21408 \dots

Solution steps

ln (\frac{π}{4}) \frac{π}{4}

Apply log rule:

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

ln (\frac{π}{4}) = ln (π) - ln (4)

= \frac{π}{4} (ln (π) - ln (4))

\frac{π}{4} = \frac{π}{2}

= \frac{π}{2} (ln (π) - ln (4))

ln (4) = 2 ln (2)

= \frac{π}{2} (ln (π) - 2 ln (2))

= \frac{π}{2} (ln (π) - 2 ln (2))

Apply the distributive law:

a (b - c) = ab - a c

a = \frac{π}{2}, b = ln (π), c = 2 ln (2)

= \frac{π}{2} ln (π) - \frac{π}{2} \cdot 2 ln (2)

= \frac{π}{2} ln (π) - 2 \cdot \frac{π}{2} ln (2)

2 \cdot \frac{π}{2} ln (2) = π ln (2)

= \frac{π}{2} ln (π) - π ln (2)

3 ln (17 x^{2})

ln (\frac{3.64}{23}) + \frac{2}{23} ln (23)

\frac{( - ln ( 83 ) + ln ( 175 ) )}{39}

ln (3 x^{4} y)

ln (x) + 4 ln (2 - \frac{y}{x})

What is ln(pi/4)*sqrt(pi/4) ?
The solution to ln(pi/4)*sqrt(pi/4) is (sqrt(pi))/2 ln(pi)-sqrt(pi)ln(2)