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

Lösung

vereinfachen

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

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

Schritte zur Lösung

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

s im pl i f y 2 lo g_{10} (y) + lo g_{10} (x)

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

s im pl i f y 3 lo g_{10} (x^{3} y) + 2 lo g_{10} (y z^{2})

s im pl i f y 2 lo g_{10} (x) - 5 lo g_{10} (x + 1)

s im pl i f y lo g_{3} (\frac{x ^{4}}{y ^{\frac{3}{5}}})