vereinfachen ln(1)-1/8 (ln(17/4+2)+ln(17/4))

Lösung

vereinfachen

ln (1) - \frac{1}{8} (ln (\frac{17}{4} + 2) + ln (\frac{17}{4}))

- \frac{1}{8} ln (\frac{425}{16})

Dezimale

- 0.40993 \dots

Schritte zur Lösung

ln (1) - \frac{1}{8} (ln (\frac{17}{4} + 2) + ln (\frac{17}{4}))

Wende die log Regel an:

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

ln (\frac{17}{4} + 2) + ln (\frac{17}{4}) = ln (\frac{17}{4} (\frac{17}{4} + 2))

= ln (1) - \frac{1}{8} ln (\frac{17}{4} (\frac{17}{4} + 2))

(\frac{17}{4} + 2) \frac{17}{4} = \frac{425}{16}

= ln (1) - \frac{1}{8} ln (\frac{425}{16})

Wende die log Regel an:

lo g_{a} (1) = 0

= 0 - \frac{1}{8} ln (\frac{425}{16})

0 - \frac{1}{8} ln (\frac{425}{16}) = - \frac{1}{8} ln (\frac{425}{16})

= - \frac{1}{8} ln (\frac{425}{16})

s im pl i f y ln (x + 6) + ln (x + 1)

s im pl i f y ln (1 + 3 x) - ln (1 - x)

s im pl i f y - 2 ln ∣ x ∣ + ln ∣ x + 1 ∣ + ln ∣ x - 1 ∣

s im pl i f y 22 (- \frac{1}{4} ln ∣ z + 2 ∣ + \frac{1}{4} ln ∣ z - 2 ∣)

s im pl i f y \frac{19}{13} + \frac{4}{5} ln (\frac{5}{4}) + \frac{3}{8} ln (2)