vereinfachen 4ln(x)+1/3 ln(x-3)-4ln(2x-1)-2022

Lösung

vereinfachen

4 ln (x) + \frac{1}{3} ln (x - 3) - 4 ln (2 x - 1) - 2022

ln (\frac{x ^{4} ( x - 3 ) ^{\frac{1}{3}}}{( 2 x - 1 ) ^{4}}) - 2022

Schritte zur Lösung

4 ln (x) + \frac{1}{3} ln (x - 3) - 4 ln (2 x - 1) - 2022

Wende die log Regel an:

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

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

= ln (x^{4}) + \frac{1}{3} ln (x - 3) - 4 ln (2 x - 1) - 2022

Wende die log Regel an:

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

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

= ln (x^{4}) + ln ((x - 3)^{\frac{1}{3}}) - 4 ln (2 x - 1) - 2022

Wende die log Regel an:

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

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

= ln (x^{4} (x - 3)^{\frac{1}{3}}) - 4 ln (2 x - 1) - 2022

Wende die log Regel an:

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

4 ln (2 x - 1) = ln ((2 x - 1)^{4})

= ln (x^{4} (x - 3)^{\frac{1}{3}}) - ln ((2 x - 1)^{4}) - 2022

Wende die log Regel an:

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

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

= ln (\frac{x ^{4} ( x - 3 ) ^{\frac{1}{3}}}{( 2 x - 1 ) ^{4}}) - 2022

s im pl i f y lo g_{2} (2 cos (x))

j o in \frac{1}{2} ln (\frac{y ^{2}}{x ^{2}} + 1)

s im pl i f y - lo g_{10} (3.4 \cdot 1 0^{- 5})

s im pl i f y ln (\frac{1 \cdot 1 0 ^{- 4}}{1 \cdot 1 0 ^{- 3}})

e x p an d lo g_{v} (b^{4}) (b^{9})