vereinfachen 2ln(2)+5ln(x)-1/2 ln(x+3)

Lösung

vereinfachen

2 ln (2) + 5 ln (x) - \frac{1}{2} ln (x + 3)

ln (\frac{4 x ^{5} x + 3}{x + 3})

Schritte zur Lösung

2 ln (2) + 5 ln (x) - \frac{1}{2} ln (x + 3)

Wende die log Regel an:

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

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

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

Wende die log Regel an:

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

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

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

Wende die log Regel an:

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

ln (2^{2}) + ln (x^{5}) = ln (2^{2} x^{5})

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

2^{2} = 4

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

Wende die log Regel an:

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

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

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

Wende die log Regel an:

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

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

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

Vereinfache

\frac{4 x ^{5}}{( x + 3 ) ^{\frac{1}{2}}} : \frac{4 x ^{5} x + 3}{x + 3}

= ln (\frac{4 x ^{5} x + 3}{x + 3})

s im pl i f y ln (P) - ln (- P + 1)

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

s im pl i f y - \frac{1}{4} ln (1 + 2) + \frac{1}{4} ln (1 - 2)

s im pl i f y 5.23 + lo g_{10} (\frac{1.76 \cdot 1 0 ^{- 3}}{0.00322})

s im pl i f y 4 ln (2) + 2 ln (x) - \frac{1}{2} ln (x + 2)