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Beliebt Algebra >

vereinfachen 6/5 ln|z-1|-6/5 ln|z+4|+ln|z+4|+ln|x|

Lösung

vereinfachen

\frac{6}{5} ln ∣ z - 1 ∣ - \frac{6}{5} ln ∣ z + 4 ∣ + ln ∣ z + 4 ∣ + ln ∣ x ∣

Lösung

ln (5 \frac{( z - 1 ) ^{6}}{( z + 4 ) ^{6}} ∣ z + 4 ∣ ∣ x ∣)

Schritte zur Lösung

\frac{6}{5} ln ∣ z - 1 ∣ - \frac{6}{5} ln ∣ z + 4 ∣ + ln ∣ z + 4 ∣ + ln ∣ x ∣

Wende die log Regel an:

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

\frac{6}{5} ln ∣ z - 1 ∣ = ln (∣ z - 1 ∣^{\frac{6}{5}})

= ln (∣ z - 1 ∣^{\frac{6}{5}}) - \frac{6}{5} ln ∣ z + 4 ∣ + ln ∣ z + 4 ∣ + ln ∣ x ∣

Wende die log Regel an:

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

\frac{6}{5} ln ∣ z + 4 ∣ = ln (∣ z + 4 ∣^{\frac{6}{5}})

= ln (∣ z - 1 ∣^{\frac{6}{5}}) - ln (∣ z + 4 ∣^{\frac{6}{5}}) + ln ∣ z + 4 ∣ + ln ∣ x ∣

Wende die log Regel an:

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

ln (∣ z - 1 ∣^{\frac{6}{5}}) - ln (∣ z + 4 ∣^{\frac{6}{5}}) = ln (\frac{∣ z - 1 ∣ ^{\frac{6}{5}}}{∣ z + 4 ∣ ^{\frac{6}{5}}})

= ln (\frac{∣ z - 1 ∣ ^{\frac{6}{5}}}{∣ z + 4 ∣ ^{\frac{6}{5}}}) + ln ∣ z + 4 ∣ + ln ∣ x ∣

Vereinfache

\frac{∣ z - 1 ∣ ^{\frac{6}{5}}}{∣ z + 4 ∣ ^{\frac{6}{5}}} : 5 \frac{( z - 1 ) ^{6}}{( z + 4 ) ^{6}}

= ln (5 \frac{( z - 1 ) ^{6}}{( z + 4 ) ^{6}}) + ln ∣ z + 4 ∣ + ln ∣ x ∣

Wende die log Regel an:

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

ln (5 \frac{( z - 1 ) ^{6}}{( z + 4 ) ^{6}}) + ln ∣ z + 4 ∣ = ln (5 \frac{( z - 1 ) ^{6}}{( z + 4 ) ^{6}} ∣ z + 4 ∣)

= ln (5 \frac{( z - 1 ) ^{6}}{( z + 4 ) ^{6}} ∣ z + 4 ∣) + ln ∣ x ∣

Wende die log Regel an:

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

ln (5 \frac{( z - 1 ) ^{6}}{( z + 4 ) ^{6}} ∣ z + 4 ∣) + ln ∣ x ∣ = ln (5 \frac{( z - 1 ) ^{6}}{( z + 4 ) ^{6}} ∣ x ∣ ∣ z + 4 ∣)

= ln (5 \frac{( z - 1 ) ^{6}}{( z + 4 ) ^{6}} ∣ z + 4 ∣ ∣ x ∣)

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