vereinfachen (0.287)ln(500/200)+(1.05)ln(680/980)

Lösung

vereinfachen

(0.287) ln (\frac{500}{200}) + (1.05) ln (\frac{680}{980})

ln (0.88624 \dots)

Dezimale

- 0.12075 \dots

Schritte zur Lösung

(0.287) ln (\frac{500}{200}) + (1.05) ln (\frac{680}{980})

Wende die log Regel an:

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

(0.287) ln (\frac{500}{200}) = ln ((\frac{500}{200})^{(0.287)})

= ln ((\frac{500}{200})^{(0.287)}) + (1.05) ln (\frac{680}{980})

Wende die log Regel an:

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

(1.05) ln (\frac{680}{980}) = ln ((\frac{680}{980})^{(1.05)})

= ln ((\frac{500}{200})^{(0.287)}) + ln ((\frac{680}{980})^{(1.05)})

Wende die log Regel an:

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

ln ((\frac{500}{200})^{(0.287)}) + ln ((\frac{680}{980})^{(1.05)}) = ln ((\frac{680}{980})^{1.05} (\frac{500}{200})^{0.287})

= ln ((\frac{680}{980})^{1.05} (\frac{500}{200})^{0.287})

(\frac{500}{200})^{(0.287)} (\frac{680}{980})^{(1.05)} = 0.88624 \dots

= ln (0.88624 \dots)

s im pl i f y ln (\frac{0.42}{- 0.23})

s im pl i f y ln (a) - 6 ln (b) + 3 ln (c)

s im pl i f y 20 lo g_{10} (\frac{4 π}{3 \cdot 1 0 ^{8}})

s im pl i f y ln (x^{4}) + ln (x^{5})

s im pl i f y - lo g_{10} (2.7 \cdot 1 0^{- 11})