vereinfachen-1/7 ln|100+6|+1/7 ln|100-1|

Lösung

vereinfachen

- \frac{1}{7} ln ∣ 100 + 6 ∣ + \frac{1}{7} ln ∣ 100 - 1 ∣

\frac{1}{7} ln (\frac{99}{106})

Dezimale

- 0.00975 \dots

Schritte zur Lösung

- \frac{1}{7} ln ∣ 100 + 6 ∣ + \frac{1}{7} ln ∣ 100 - 1 ∣

Wende die log Regel an:

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

\frac{1}{7} ln ∣ 100 + 6 ∣ = ln (∣ 100 + 6 ∣^{\frac{1}{7}})

= - ln (∣ 100 + 6 ∣^{\frac{1}{7}}) + \frac{1}{7} ln ∣ 100 - 1 ∣

Wende die log Regel an:

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

\frac{1}{7} ln ∣ 100 - 1 ∣ = ln (∣ 100 - 1 ∣^{\frac{1}{7}})

= - ln (∣ 100 + 6 ∣^{\frac{1}{7}}) + ln (∣ 100 - 1 ∣^{\frac{1}{7}})

Wende die log Regel an:

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

ln (∣ 100 - 1 ∣^{\frac{1}{7}}) - ln (∣ 100 + 6 ∣^{\frac{1}{7}}) = ln (\frac{∣ 100 - 1 ∣ ^{\frac{1}{7}}}{∣ 100 + 6 ∣ ^{\frac{1}{7}}})

= ln (\frac{∣ 100 - 1 ∣ ^{\frac{1}{7}}}{∣ 100 + 6 ∣ ^{\frac{1}{7}}})

\frac{∣ 100 - 1 ∣ ^{\frac{1}{7}}}{∣ 100 + 6 ∣ ^{\frac{1}{7}}} = 7 \frac{99}{106}

= ln (7 \frac{99}{106})

Schreibe um

= ln ((\frac{99}{106})^{\frac{1}{7}})

Wende log Regel an

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

angenommen

x \geq 0

= \frac{1}{7} ln (\frac{99}{106})

e x p an d lo g_{d} (\frac{a b ^{2}}{c ^{3}})

s im pl i f y ln (\frac{sin ( x )}{x ^{3} - 2})

s im pl i f y ln (8 e) - ln (6 e) - ln (e^{2})

s im pl i f y ln (- 23 i)

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