vereinfachen 3ln(x-4)+2ln(3)-1/2 ln(y)

Lösung

vereinfachen

3 ln (x - 4) + 2 ln (3) - \frac{1}{2} ln (y)

ln (\frac{9 y ( x - 4 ) ^{3}}{y})

Schritte zur Lösung

3 ln (x - 4) + 2 ln (3) - \frac{1}{2} ln (y)

Wende die log Regel an:

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

3 ln (x - 4) = ln ((x - 4)^{3})

= ln ((x - 4)^{3}) + 2 ln (3) - \frac{1}{2} ln (y)

Wende die log Regel an:

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

2 ln (3) = ln (3^{2})

= ln ((x - 4)^{3}) + ln (3^{2}) - \frac{1}{2} ln (y)

Wende die log Regel an:

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

ln ((x - 4)^{3}) + ln (3^{2}) = ln (3^{2} (x - 4)^{3})

= ln (3^{2} (x - 4)^{3}) - \frac{1}{2} ln (y)

3^{2} = 9

= ln (9 (x - 4)^{3}) - \frac{1}{2} ln (y)

Wende die log Regel an:

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

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

= ln (9 (x - 4)^{3}) - ln (y^{\frac{1}{2}})

Wende die log Regel an:

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

ln (9 (x - 4)^{3}) - ln (y^{\frac{1}{2}}) = ln (\frac{9 ( x - 4 ) ^{3}}{y ^{\frac{1}{2}}})

= ln (\frac{9 ( x - 4 ) ^{3}}{y ^{\frac{1}{2}}})

Vereinfache

\frac{9 ( x - 4 ) ^{3}}{y ^{\frac{1}{2}}} : \frac{9 y ( x - 4 ) ^{3}}{y}

= ln (\frac{9 y ( x - 4 ) ^{3}}{y})

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

s im pl i f y ln (\frac{15}{2})

e x p an d lo g_{10} (\frac{x ^{2}}{y})

e x p an d ln ((x y)^{4})

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