vereinfachen ln(3)(-1-1/2-1/8+3/4)+ln(2)(1-1/4-3/4)

Lösung

vereinfachen

ln (3) (- 1 - \frac{1}{2} - \frac{1}{8} + \frac{3}{4}) + ln (2) (1 - \frac{1}{4} - \frac{3}{4})

ln (\frac{8 3}{3})

Dezimale

- 0.96128 \dots

Schritte zur Lösung

ln (3) (- 1 - \frac{1}{2} - \frac{1}{8} + \frac{3}{4}) + ln (2) (1 - \frac{1}{4} - \frac{3}{4})

Wende die log Regel an:

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

ln (3) (\frac{3}{4} - 1 - \frac{1}{2} - \frac{1}{8}) = ln (3^{(\frac{3}{4} - 1 - \frac{1}{2} - \frac{1}{8})})

= ln (3^{(\frac{3}{4} - 1 - \frac{1}{2} - \frac{1}{8})}) + ln (2) (1 - \frac{1}{4} - \frac{3}{4})

Wende die log Regel an:

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

ln (2) (1 - \frac{1}{4} - \frac{3}{4}) = ln (2^{(1 - \frac{1}{4} - \frac{3}{4})})

= ln (3^{(\frac{3}{4} - 1 - \frac{1}{2} - \frac{1}{8})}) + ln (2^{(1 - \frac{1}{4} - \frac{3}{4})})

Wende die log Regel an:

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

ln (3^{(- 1 - \frac{1}{2} - \frac{1}{8} + \frac{3}{4})}) + ln (2^{(1 - \frac{1}{4} - \frac{3}{4})}) = ln (3^{\frac{3}{4} - 1 - \frac{1}{2} - \frac{1}{8}} \cdot 2^{1 - \frac{1}{4} - \frac{3}{4}})

= ln (3^{\frac{3}{4} - 1 - \frac{1}{2} - \frac{1}{8}} \cdot 2^{1 - \frac{1}{4} - \frac{3}{4}})

3^{(- 1 - \frac{1}{2} - \frac{1}{8} + \frac{3}{4})} \cdot 2^{(1 - \frac{1}{4} - \frac{3}{4})} = \frac{8 3}{3}

= ln (\frac{8 3}{3})

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