vereinfachen ln(2/(sin(θ)))-ln(1/(sin(θ)))

Lösung

vereinfachen

ln (\frac{2}{sin ( θ )}) - ln (\frac{1}{sin ( θ )})

ln (2)

Dezimale

0.69314 \dots

Schritte zur Lösung

ln (\frac{2}{sin ( θ )}) - ln (\frac{1}{sin ( θ )})

Wende die log Regel an:

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

ln (\frac{2}{sin ( θ )}) - ln (\frac{1}{sin ( θ )}) = ln (\frac{\frac{2}{s i n ( θ )}}{\frac{1}{s i n ( θ )}})

= ln (\frac{\frac{2}{s i n ( θ )}}{\frac{1}{s i n ( θ )}})

\frac{\frac{2}{s i n ( θ )}}{\frac{1}{s i n ( θ )}} = 2

= ln (2)

s im pl i f y 2 ln (2) - 2 ln (7)

j o in \frac{15 ln ( \frac{59}{38} )}{ln ( 2 )}

j o in \frac{81}{4} ln (3)

s im pl i f y \frac{1}{5} ln (\frac{2}{3})

j o in - \frac{1}{2} lo g_{10} (2)