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Beliebt >

vereinfachen 5ln(x)-5/3 ln(y)-6ln(w^2)+9ln(z)

Lösung

vereinfachen

5 ln (x) - \frac{5}{3} ln (y) - 6 ln (w^{2}) + 9 ln (z)

ln (\frac{x ^{5} z ^{9}}{w ^{12} y ^{\frac{5}{3}}})

Schritte zur Lösung

5 ln (x) - \frac{5}{3} ln (y) - 6 ln (w^{2}) + 9 ln (z)

Wende die log Regel an:

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

5 ln (x) = ln (x^{5})

= ln (x^{5}) - \frac{5}{3} ln (y) - 6 ln (w^{2}) + 9 ln (z)

Wende die log Regel an:

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

\frac{5}{3} ln (y) = ln (y^{\frac{5}{3}})

= ln (x^{5}) - ln (y^{\frac{5}{3}}) - 6 ln (w^{2}) + 9 ln (z)

Wende die log Regel an:

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

ln (x^{5}) - ln (y^{\frac{5}{3}}) = ln (\frac{x ^{5}}{y ^{\frac{5}{3}}})

= ln (\frac{x ^{5}}{y ^{\frac{5}{3}}}) - 6 ln (w^{2}) + 9 ln (z)

Wende die log Regel an:

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

6 ln (w^{2}) = ln ((w^{2})^{6})

= ln (\frac{x ^{5}}{y ^{\frac{5}{3}}}) - ln ((w^{2})^{6}) + 9 ln (z)

Wende die log Regel an:

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

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

= ln \frac{\frac{x ^{5}}{y ^{\frac{5}{3}}}}{( w ^{2} ) ^{6}} + 9 ln (z)

Vereinfache

\frac{\frac{x ^{5}}{y ^{\frac{5}{3}}}}{( w ^{2} ) ^{6}} : \frac{x ^{5}}{w ^{12} y ^{\frac{5}{3}}}

= ln (\frac{x ^{5}}{w ^{12} y ^{\frac{5}{3}}}) + 9 ln (z)

Wende die log Regel an:

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

9 ln (z) = ln (z^{9})

= ln (\frac{x ^{5}}{w ^{12} y ^{\frac{5}{3}}}) + ln (z^{9})

Wende die log Regel an:

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

ln (\frac{x ^{5}}{w ^{12} y ^{\frac{5}{3}}}) + ln (z^{9}) = ln (\frac{x ^{5}}{w ^{12} y ^{\frac{5}{3}}} z^{9})

= ln (\frac{x ^{5}}{w ^{12} y ^{\frac{5}{3}}} z^{9})

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= ln (\frac{x ^{5} z ^{9}}{w ^{12} y ^{\frac{5}{3}}})

lo g_{5} (3 x)

\frac{1}{2} lo g_{10} (a) + 3 lo g_{10} (b)

lo g_{3} (x + 1) - lo g_{3} (x^{2} - 1)

lo g_{b} (z^{6} y)

lo g_{4} (\frac{a ( x + 3 ) ^{3}}{a - b ^{3}})