vereinfachen 1/2 ln((x^2+(y-1)^2)/(x^2))+ln(x)

Lösung

vereinfachen

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

ln (x^{2} + (y - 1)^{2})

Schritte zur Lösung

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

Wende die log Regel an:

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

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

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

Wende die log Regel an:

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

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

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

Vereinfache

(\frac{x ^{2} + ( y - 1 ) ^{2}}{x ^{2}})^{\frac{1}{2}} x : x^{2} + (y - 1)^{2}

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

s im pl i f y 2 ln (2) - 2 ln (3)

j o in \frac{3 ln ( 2 )}{ln ( \frac{3}{2} )}

s im pl i f y 2 lo g_{10} (0.000001) + 2 lo g_{10} (0.001)

s im pl i f y ln (\frac{1.61}{3.792})

s im pl i f y \frac{1}{2} lo g_{10} (z) - \frac{1}{4} lo g_{10} (y)