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

Lösung

vereinfachen

\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}

Dezimale

0.21290 \dots

Schritte zur Lösung

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

Wende die log Regel an:

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}

Wende die log Regel an:

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}

Wende die log Regel an:

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{2 ^{\frac{1}{4}}}{( \frac{4}{3} ) ^{\frac{1}{8}}} = 83

= ln (83) + \frac{π}{24 3}

ln (83) = \frac{1}{8} ln (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}

s im pl i f y lo g_{5} (\frac{\frac{3 x + 1 ^{3}}{2 x - 1 ^{2}}}{x})

s im pl i f y ln (\frac{12 \cdot 1 0 ^{6}}{1 \cdot 1 0 ^{8}})

s im pl i f y 1 + ln (\frac{1}{2})

s im pl i f y 5 ln (\frac{5}{3})

s im pl i f y ln ((x + 1)^{2} \frac{d y}{d x})