vereinfachen 1.05ln(700/1450)+0.287ln(50/2)+50/573

Lösung

vereinfachen

1.05 ln (\frac{700}{1450}) + 0.287 ln (\frac{50}{2}) + \frac{50}{573}

ln (1.17253 \dots) + \frac{50}{573}

Dezimale

0.24642 \dots

Schritte zur Lösung

1.05 ln (\frac{700}{1450}) + 0.287 ln (\frac{50}{2}) + \frac{50}{573}

Wende die log Regel an:

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

1.05 ln (\frac{700}{1450}) = ln ((\frac{700}{1450})^{1.05})

= ln ((\frac{700}{1450})^{1.05}) + 0.287 ln (\frac{50}{2}) + \frac{50}{573}

Wende die log Regel an:

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

0.287 ln (\frac{50}{2}) = ln ((\frac{50}{2})^{0.287})

= ln ((\frac{700}{1450})^{1.05}) + ln ((\frac{50}{2})^{0.287}) + \frac{50}{573}

Wende die log Regel an:

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

ln ((\frac{700}{1450})^{1.05}) + ln ((\frac{50}{2})^{0.287}) = ln ((\frac{50}{2})^{0.287} (\frac{700}{1450})^{1.05})

= ln ((\frac{50}{2})^{0.287} (\frac{700}{1450})^{1.05}) + \frac{50}{573}

(\frac{700}{1450})^{1.05} (\frac{50}{2})^{0.287} = 1.17253 \dots

= ln (1.17253 \dots) + \frac{50}{573}

s im pl i f y ln (\frac{e ^{x}}{e ^{x} - 1})

s im pl i f y \frac{5}{2} ln (x) + \frac{7}{2} ln (y) - ln (z) - 4 ln (z)

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s im pl i f y 4.74 - lo g_{10} (\frac{1}{1.8597})

s im pl i f y ln (2 e^{- 1})