vereinfachen 5ln(2)+3ln(x)-1/2 ln(x+7)

Lösung

vereinfachen

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

ln (\frac{32 x ^{3} x + 7}{x + 7})

Schritte zur Lösung

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

Wende die log Regel an:

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

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

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

Wende die log Regel an:

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

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

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

Wende die log Regel an:

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

ln (2^{5}) + ln (x^{3}) = ln (2^{5} x^{3})

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

2^{5} = 32

= ln (32 x^{3}) - \frac{1}{2} ln (x + 7)

Wende die log Regel an:

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

\frac{1}{2} ln (x + 7) = ln ((x + 7)^{\frac{1}{2}})

= ln (32 x^{3}) - ln ((x + 7)^{\frac{1}{2}})

Wende die log Regel an:

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

ln (32 x^{3}) - ln ((x + 7)^{\frac{1}{2}}) = ln (\frac{32 x ^{3}}{( x + 7 ) ^{\frac{1}{2}}})

= ln (\frac{32 x ^{3}}{( x + 7 ) ^{\frac{1}{2}}})

Vereinfache

\frac{32 x ^{3}}{( x + 7 ) ^{\frac{1}{2}}} : \frac{32 x ^{3} x + 7}{x + 7}

= ln (\frac{32 x ^{3} x + 7}{x + 7})

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

e x p an d lo g_{9} ((\frac{3 ^{3}}{7})^{4})

s im pl i f y 2 ln ∣ ln (x) ∣ + ln (x)

s im pl i f y \frac{\frac{3}{l n ( 7 ) - l n ( 4 )}}{3 x + 4}

s im pl i f y - lo g_{10} (7.1 \cdot 1 0^{- 7})