vereinfachen 2ln(x^4)-3ln(x^2)+4ln(x^3)

Lösung

vereinfachen

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

ln (x^{14})

Schritte zur Lösung

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

Wende die log Regel an:

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

2 ln (x^{4}) = ln ((x^{4})^{2})

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

Wende die log Regel an:

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

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

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

Wende die log Regel an:

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

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

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

Vereinfache

\frac{( x ^{4} ) ^{2}}{( x ^{2} ) ^{3}} : x^{2}

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

Wende die log Regel an:

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

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

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

Wende die log Regel an:

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

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

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

Vereinfache

x^{2} (x^{3})^{4} : x^{14}

= ln (x^{14})

s im pl i f y ln (0.906 \cdot 0.921 \cdot 0.971 \cdot 0.598 \cdot 0.983 \cdot 0.937)

s im pl i f y \frac{d ^{4}}{d x ^{4}} (e^{- 4 x}) + 6 ln (3 x^{5})

s im pl i f y ln (y) - \frac{1}{2} ln (y - 1) - \frac{1}{2} ln (y + 1)

s im pl i f y - 2 ln ∣ l + d ∣ + ln ∣ d ∣ + ln ∣ 2 l + d ∣

s im pl i f y lo g_{4} (x^{2} - 1) - 5 lo g_{4} (x - 1)