vereinfachen 3/2 ln(4x^6)-4/5 ln(2y^{10})

Lösung

vereinfachen

\frac{3}{2} ln (4 x^{6}) - \frac{4}{5} ln (2 y^{10})

ln (\frac{4 5 2 x ^{9}}{y ^{8}})

Schritte zur Lösung

\frac{3}{2} ln (4 x^{6}) - \frac{4}{5} ln (2 y^{10})

Wende die log Regel an:

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

\frac{3}{2} ln (4 x^{6}) = ln ((4 x^{6})^{\frac{3}{2}})

= ln ((4 x^{6})^{\frac{3}{2}}) - \frac{4}{5} ln (2 y^{10})

Wende die log Regel an:

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

\frac{4}{5} ln (2 y^{10}) = ln ((2 y^{10})^{\frac{4}{5}})

= ln ((4 x^{6})^{\frac{3}{2}}) - ln ((2 y^{10})^{\frac{4}{5}})

Wende die log Regel an:

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

ln ((4 x^{6})^{\frac{3}{2}}) - ln ((2 y^{10})^{\frac{4}{5}}) = ln \frac{( 4 x ^{6} ) ^{\frac{3}{2}}}{( 2 y ^{10} ) ^{\frac{4}{5}}}

= ln \frac{( 4 x ^{6} ) ^{\frac{3}{2}}}{( 2 y ^{10} ) ^{\frac{4}{5}}}

Vereinfache

\frac{( 4 x ^{6} ) ^{\frac{3}{2}}}{( 2 y ^{10} ) ^{\frac{4}{5}}} : \frac{4 5 2 x ^{9}}{y ^{8}}

= ln (\frac{4 5 2 x ^{9}}{y ^{8}})

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