vereinfachen 63/17 ln|-4|-63/17 ln|-8|

Lösung

vereinfachen

\frac{63}{17} ln ∣ - 4 ∣ - \frac{63}{17} ln ∣ - 8 ∣

ln (\frac{2 ^{\frac{5}{17}}}{2 ^{4}})

Dezimale

- 2.56872 \dots

Schritte zur Lösung

\frac{63}{17} ln ∣ - 4 ∣ - \frac{63}{17} ln ∣ - 8 ∣

Wende die log Regel an:

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

\frac{63}{17} ln ∣ - 4 ∣ = ln (∣ - 4 ∣^{\frac{63}{17}})

= ln (∣ - 4 ∣^{\frac{63}{17}}) - \frac{63}{17} ln ∣ - 8 ∣

Wende die log Regel an:

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

\frac{63}{17} ln ∣ - 8 ∣ = ln (∣ - 8 ∣^{\frac{63}{17}})

= ln (∣ - 4 ∣^{\frac{63}{17}}) - ln (∣ - 8 ∣^{\frac{63}{17}})

Wende die log Regel an:

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

ln (∣ - 4 ∣^{\frac{63}{17}}) - ln (∣ - 8 ∣^{\frac{63}{17}}) = ln (\frac{∣ - 4 ∣ ^{\frac{63}{17}}}{∣ - 8 ∣ ^{\frac{63}{17}}})

= ln (\frac{∣ - 4 ∣ ^{\frac{63}{17}}}{∣ - 8 ∣ ^{\frac{63}{17}}})

\frac{∣ - 4 ∣ ^{\frac{63}{17}}}{∣ - 8 ∣ ^{\frac{63}{17}}} = \frac{2 ^{\frac{5}{17}}}{16}

= ln (\frac{2 ^{\frac{5}{17}}}{16})

\frac{2 ^{\frac{5}{17}}}{16} = \frac{2 ^{\frac{5}{17}}}{2 ^{4}}

= ln (\frac{2 ^{\frac{5}{17}}}{2 ^{4}})

e x p an d lo g_{8} (3 x^{3})

s im pl i f y lo g_{\frac{1}{2}} (\frac{1}{2000})

s im pl i f y \frac{π}{8} (ln (13) - ln (5))

s im pl i f y ln (\frac{29000}{24000})

s im pl i f y ln (2) - \frac{3}{2} + ln (\frac{5}{2}) - \frac{21}{50}