vereinfachen-0.1ln(0.1)-(1-0.1)ln(1-0.1)

Lösung

vereinfachen

- 0.1 ln (0.1) - (1 - 0.1) ln (1 - 0.1)

- ln (0.72246 \dots)

Dezimale

0.32508 \dots

Schritte zur Lösung

- 0.1 ln (0.1) - (1 - 0.1) ln (1 - 0.1)

Wende die log Regel an:

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

0.1 ln (0.1) = ln (0. 1^{0.1})

= - ln (0. 1^{0.1}) - ln (1 - 0.1) (1 - 0.1)

Wende die log Regel an:

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

ln (1 - 0.1) (1 - 0.1) = ln ((1 - 0.1)^{(1 - 0.1)})

= - ln (0. 1^{0.1}) - ln ((1 - 0.1)^{(1 - 0.1)})

Schreibe

- ln (0. 1^{0.1}) - ln ((1 - 0.1)^{(1 - 0.1)})

um:

- (ln (0. 1^{0.1}) + ln ((1 - 0.1)^{(1 - 0.1)}))

= - (ln (0. 1^{0.1}) + ln ((1 - 0.1)^{(1 - 0.1)}))

Wende die log Regel an:

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

ln (0. 1^{0.1}) + ln ((1 - 0.1)^{(1 - 0.1)}) = ln (0. 1^{0.1} (1 - 0.1)^{1 - 0.1})

= - ln (0. 1^{0.1} (1 - 0.1)^{1 - 0.1})

0. 1^{0.1} (1 - 0.1)^{(1 - 0.1)} = 0.72246 \dots

= - ln (0.72246 \dots)

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

s im pl i f y ln (e^{x^{2}} x)

s im pl i f y 2 ln ∣ 2 ∣ - 2 ln \frac{1}{4}

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

s im pl i f y - lo g_{10} (3.52 x 1 0^{- 4})