What is 1/4 ln(2)-1/8 ln(4/3)+pi/(24sqrt(3)) ?

The solution to 1/4 ln(2)-1/8 ln(4/3)+pi/(24sqrt(3)) is 1/8 ln(3)+(sqrt(3)pi)/(72)

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simplify 1/4 ln(2)-1/8 ln(4/3)+pi/(24sqrt(3))

simplify

\frac{1}{4} ln (2) - \frac{1}{8} ln (\frac{4}{3}) + \frac{π}{24 3}

\frac{1}{8} ln (3) + \frac{3 π}{72}

Decimal Notation

0.21290 \dots

Solution steps

\frac{1}{4} ln (2) - \frac{1}{8} ln (\frac{4}{3}) + \frac{π}{24 3}

Apply log rule:

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

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

= ln (2^{\frac{1}{4}}) - \frac{1}{8} ln (\frac{4}{3}) + \frac{π}{24 3}

Apply log rule:

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

\frac{1}{8} ln (\frac{4}{3}) = ln ((\frac{4}{3})^{\frac{1}{8}})

= ln (2^{\frac{1}{4}}) - ln ((\frac{4}{3})^{\frac{1}{8}}) + \frac{π}{24 3}

Apply log rule:

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

ln (2^{\frac{1}{4}}) - ln ((\frac{4}{3})^{\frac{1}{8}}) = ln \frac{2 ^{\frac{1}{4}}}{( \frac{4}{3} ) ^{\frac{1}{8}}}

= ln \frac{2 ^{\frac{1}{4}}}{( \frac{4}{3} ) ^{\frac{1}{8}}} + \frac{π}{24 3}

= \frac{1}{8} ln (3) + \frac{π}{24 3}

\frac{π}{24 3} = \frac{3 π}{72}

= \frac{1}{8} ln (3) + \frac{3 π}{72}

lo g_{5} (\frac{\frac{3 x + 1 ^{3}}{2 x - 1 ^{2}}}{x})

ln (\frac{7163}{7})

ln (\frac{12 \cdot 1 0 ^{6}}{1 \cdot 1 0 ^{8}})

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

ln (3.8 2.2 x + 5.4)

What is 1/4 ln(2)-1/8 ln(4/3)+pi/(24sqrt(3)) ?
The solution to 1/4 ln(2)-1/8 ln(4/3)+pi/(24sqrt(3)) is 1/8 ln(3)+(sqrt(3)pi)/(72)