vereinfachen 3/6ln((z-3)/(z+3))-1/2ln(z^2-9)

Lösung

vereinfachen

\frac{3}{6} \cdot ln (\frac{z - 3}{z + 3}) - \frac{1}{2} \cdot ln (z^{2} - 9)

ln \frac{( z ^{2} - 9 ) ^{\frac{1}{2}} z - 3 z + 3}{( z + 3 ) ^{2} ( z - 3 )}

Schritte zur Lösung

\frac{3}{6} ln (\frac{z - 3}{z + 3}) - \frac{1}{2} ln (z^{2} - 9)

Wende die log Regel an:

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

\frac{3}{6} ln (\frac{z - 3}{z + 3}) = ln ((\frac{z - 3}{z + 3})^{\frac{3}{6}})

= ln ((\frac{z - 3}{z + 3})^{\frac{3}{6}}) - \frac{1}{2} ln (z^{2} - 9)

Wende die log Regel an:

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

\frac{1}{2} ln (z^{2} - 9) = ln ((z^{2} - 9)^{\frac{1}{2}})

= ln ((\frac{z - 3}{z + 3})^{\frac{3}{6}}) - ln ((z^{2} - 9)^{\frac{1}{2}})

Wende die log Regel an:

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

ln ((\frac{z - 3}{z + 3})^{\frac{3}{6}}) - ln ((z^{2} - 9)^{\frac{1}{2}}) = ln \frac{( \frac{z - 3}{z + 3} ) ^{\frac{3}{6}}}{( z ^{2} - 9 ) ^{\frac{1}{2}}}

= ln \frac{( \frac{z - 3}{z + 3} ) ^{\frac{3}{6}}}{( z ^{2} - 9 ) ^{\frac{1}{2}}}

Vereinfache

\frac{( \frac{z - 3}{z + 3} ) ^{\frac{3}{6}}}{( z ^{2} - 9 ) ^{\frac{1}{2}}} : \frac{( z ^{2} - 9 ) ^{\frac{1}{2}} z - 3 z + 3}{( z + 3 ) ^{2} ( z - 3 )}

= ln \frac{( z ^{2} - 9 ) ^{\frac{1}{2}} z - 3 z + 3}{( z + 3 ) ^{2} ( z - 3 )}

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