vereinfachen 1/2 ln|8.7+4|-1/2 ln|8.7+6|+C

Lösung

vereinfachen

\frac{1}{2} ln ∣ 8.7 + 4 ∣ - \frac{1}{2} ln ∣ 8.7 + 6 ∣ + C

ln (0.92948 \dots) + C

Schritte zur Lösung

\frac{1}{2} ln ∣ 8.7 + 4 ∣ - \frac{1}{2} ln ∣ 8.7 + 6 ∣ + C

Wende die log Regel an:

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

\frac{1}{2} ln ∣ 4 + 8.7 ∣ = ln (∣ 4 + 8.7 ∣^{\frac{1}{2}})

= ln (∣ 4 + 8.7 ∣^{\frac{1}{2}}) - \frac{1}{2} ln ∣ 6 + 8.7 ∣ + C

Wende die log Regel an:

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

\frac{1}{2} ln ∣ 6 + 8.7 ∣ = ln (∣ 6 + 8.7 ∣^{\frac{1}{2}})

= ln (∣ 4 + 8.7 ∣^{\frac{1}{2}}) - ln (∣ 6 + 8.7 ∣^{\frac{1}{2}}) + C

Wende die log Regel an:

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

ln (∣ 8.7 + 4 ∣^{\frac{1}{2}}) - ln (∣ 8.7 + 6 ∣^{\frac{1}{2}}) = ln (\frac{∣ 4 + 8.7 ∣ ^{\frac{1}{2}}}{∣ 6 + 8.7 ∣ ^{\frac{1}{2}}})

= ln (\frac{∣ 4 + 8.7 ∣ ^{\frac{1}{2}}}{∣ 6 + 8.7 ∣ ^{\frac{1}{2}}}) + C

\frac{∣ 8.7 + 4 ∣ ^{\frac{1}{2}}}{∣ 8.7 + 6 ∣ ^{\frac{1}{2}}} = 0.92948 \dots

= ln (0.92948 \dots) + C

j o in \frac{1}{4} \cdot ln (2)

s im pl i f y ln (\frac{3}{e})

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s im pl i f y \frac{1}{5} \cdot lo g_{7} (x) - \frac{1}{3} \cdot lo g_{7} (y)

s im pl i f y 10 - 12 ln (x) - 18 ln (y)