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

Lösung

vereinfachen

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

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

Schritte zur Lösung

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

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 + 5)

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 + 5)

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 + 5)

2^{2} = 4

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

Wende die log Regel an:

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

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

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

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

Vereinfache

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

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

s im pl i f y ln (16 e^{6} z)

s im pl i f y lo g_{3} (\frac{3 4}{q ^{2} y})

s im pl i f y lo g_{4} (\frac{x ^{5}}{y ^{8}})

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

s im pl i f y lo g_{10} (x (x^{2} + 2)^{\frac{1}{2}})