vereinfachen 1.0034ln(523/303)-0.287ln(800/95)

Lösung

vereinfachen

1.0034 \cdot ln (\frac{523}{303}) - 0.287 \cdot ln (\frac{800}{95})

ln (0.93817 \dots)

Dezimale

- 0.06381 \dots

Schritte zur Lösung

1.0034 ln (\frac{523}{303}) - 0.287 ln (\frac{800}{95})

Wende die log Regel an:

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

1.0034 ln (\frac{523}{303}) = ln ((\frac{523}{303})^{1.0034})

= ln ((\frac{523}{303})^{1.0034}) - 0.287 ln (\frac{800}{95})

Wende die log Regel an:

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

0.287 ln (\frac{800}{95}) = ln ((\frac{800}{95})^{0.287})

= ln ((\frac{523}{303})^{1.0034}) - ln ((\frac{800}{95})^{0.287})

Wende die log Regel an:

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

ln ((\frac{523}{303})^{1.0034}) - ln ((\frac{800}{95})^{0.287}) = ln (\frac{( \frac{523}{303} ) ^{1.0034}}{( \frac{800}{95} ) ^{0.287}})

= ln (\frac{( \frac{523}{303} ) ^{1.0034}}{( \frac{800}{95} ) ^{0.287}})

\frac{( \frac{523}{303} ) ^{1.0034}}{( \frac{800}{95} ) ^{0.287}} = 0.93817 \dots

= ln (0.93817 \dots)

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