vereinfachen 1/2 ln((x+1)/(x-1))+e^{sin(x^2)}+ln(3)

Lösung

vereinfachen

\frac{1}{2} ln (\frac{x + 1}{x - 1}) + e^{s i n (x^{2})} + ln (3)

ln ((\frac{x + 1}{x - 1})^{\frac{1}{2}} \cdot 3) + e^{s i n (x^{2})}

Schritte zur Lösung

\frac{1}{2} ln (\frac{x + 1}{x - 1}) + e^{s i n (x^{2})} + ln (3)

Wende die log Regel an:

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

\frac{1}{2} ln (\frac{x + 1}{x - 1}) = ln ((\frac{x + 1}{x - 1})^{\frac{1}{2}})

= ln ((\frac{x + 1}{x - 1})^{\frac{1}{2}}) + e^{s i n (x^{2})} + ln (3)

Wende die log Regel an:

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

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

= ln ((\frac{x + 1}{x - 1})^{\frac{1}{2}} \cdot 3) + e^{s i n (x^{2})}

e x p an d ln (x^{4})

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

s im pl i f y ln (0.15) - ln (0.25)

s im pl i f y lo g_{b} (z^{4} y)

s im pl i f y lo g_{10} (1000 x^{4} y^{6})