vereinfachen-20.96+1.045ln(e)+3.33ln(g)-0.165ln(g^2)

Lösung

vereinfachen

- 20.96 + 1.045 ln (e) + 3.33 ln (g) - 0.165 ln (g^{2})

ln (g^{3}) - 19.915

Schritte zur Lösung

- 20.96 + 1.045 ln (e) + 3.33 ln (g) - 0.165 ln (g^{2})

Wende die log Regel an:

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

3.33 ln (g) = ln (g^{3.33})

= - 20.96 + 1.045 ln (e) + ln (g^{3.33}) - 0.165 ln (g^{2})

Wende die log Regel an:

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

0.165 ln (g^{2}) = ln ((g^{2})^{0.165})

= - 20.96 + 1.045 ln (e) + ln (g^{3.33}) - ln ((g^{2})^{0.165})

Wende die log Regel an:

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

ln (g^{3.33}) - ln ((g^{2})^{0.165}) = ln (\frac{g ^{3.33}}{( g ^{2} ) ^{0.165}})

= - 20.96 + 1.045 ln (e) + ln (\frac{g ^{3.33}}{( g ^{2} ) ^{0.165}})

Vereinfache

\frac{g ^{3.33}}{( g ^{2} ) ^{0.165}} : g^{3}

= - 20.96 + 1.045 ln (e) + ln (g^{3})

1.045 ln (e) = 1.045

= - 20.96 + 1.045 + ln (g^{3})

Addiere/Subtrahiere die Zahlen:

- 20.96 + 1.045 = - 19.915

= ln (g^{3}) - 19.915

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