What is 1/(2pi)[ 1/4 ln(3/2)+ln(4/3)] ?

The solution to 1/(2pi)[ 1/4 ln(3/2)+ln(4/3)] is (ln((2*2^{3/4}\sqrt[4]{3})/3))/(2pi)

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simplify 1/(2pi)[ 1/4 ln(3/2)+ln(4/3)]

simplify

\frac{1}{2 π} [\frac{1}{4} ln (\frac{3}{2}) + ln (\frac{4}{3})]

Decimal Notation

0.06191 \dots

Solution steps

\frac{1}{2 π} [\frac{1}{4} ln (\frac{3}{2}) + ln (\frac{4}{3})]

Apply log rule:

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

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

= \frac{1}{2 π} [ln (\frac{4}{3}) + ln ((\frac{3}{2})^{\frac{1}{4}})]

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

Remove parentheses:

(a) = a

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

Multiply:

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

ln (22.08553 - 2) + 3 ln (8.905 - 1)

ln (\frac{4 k + 1}{4 k - 1})

ln (90) - ln (80)

- ln (x) - \frac{1}{2} ln (y)

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

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