vereinfachen (4ln(x-6)+ln(x^2+6)-7ln(x+3))^{1/5}

Lösung

vereinfachen

(4 ln (x - 6) + ln (x^{2} + 6) - 7 ln (x + 3))^{\frac{1}{5}}

ln^{\frac{1}{5}} (\frac{( x - 6 ) ^{4} ( x ^{2} + 6 )}{( x + 3 ) ^{7}})

Schritte zur Lösung

(4 ln (x - 6) + ln (x^{2} + 6) - 7 ln (x + 3))^{\frac{1}{5}}

Wende die log Regel an:

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

4 ln (x - 6) = ln ((x - 6)^{4})

= (ln ((x - 6)^{4}) + ln (x^{2} + 6) - 7 ln (x + 3))^{\frac{1}{5}}

Wende die log Regel an:

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

ln ((x - 6)^{4}) + ln (x^{2} + 6) = ln ((x - 6)^{4} (x^{2} + 6))

= (ln ((x - 6)^{4} (x^{2} + 6)) - 7 ln (x + 3))^{\frac{1}{5}}

Wende die log Regel an:

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

7 ln (x + 3) = ln ((x + 3)^{7})

= (ln ((x - 6)^{4} (x^{2} + 6)) - ln ((x + 3)^{7}))^{\frac{1}{5}}

Wende die log Regel an:

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

ln ((x - 6)^{4} (x^{2} + 6)) - ln ((x + 3)^{7}) = ln (\frac{( x - 6 ) ^{4} ( x ^{2} + 6 )}{( x + 3 ) ^{7}})

= ln^{\frac{1}{5}} (\frac{( x - 6 ) ^{4} ( x ^{2} + 6 )}{( x + 3 ) ^{7}})

s im pl i f y 200 - 160 (2 ln (3) - 2 ln (2))

s im pl i f y 2 lo g_{10} (5.6) + 4 lo g_{10} (3.5)

s im pl i f y \frac{1}{2} ln (2 \cdot 9.6 + 1) + 2 ln (9.6 - 1)

s im pl i f y 3 lo g_{10} (2) - lo g_{10} (4) + 2 lo g_{10} (5)

s im pl i f y lo g_{e} (\frac{a + x}{x})