vereinfachen 1/2 ln(2(7.1)+1)+2ln(7.1-1)

Lösung

vereinfachen

\frac{1}{2} ln (2 (7.1) + 1) + 2 ln (7.1 - 1)

ln (145.07128 \dots)

Dezimale

4.97722 \dots

Schritte zur Lösung

\frac{1}{2} ln (2 (7.1) + 1) + 2 ln (7.1 - 1)

Wende die log Regel an:

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

\frac{1}{2} ln (2 (7.1) + 1) = ln ((2 (7.1) + 1)^{\frac{1}{2}})

= ln ((2 (7.1) + 1)^{\frac{1}{2}}) + 2 ln (7.1 - 1)

Wende die log Regel an:

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

2 ln (7.1 - 1) = ln ((7.1 - 1)^{2})

= ln ((2 (7.1) + 1)^{\frac{1}{2}}) + ln ((7.1 - 1)^{2})

Wende die log Regel an:

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

ln ((2 (7.1) + 1)^{\frac{1}{2}}) + ln ((7.1 - 1)^{2}) = ln ((7.1 - 1)^{2} (2 \cdot 7.1 + 1)^{\frac{1}{2}})

= ln ((7.1 - 1)^{2} (2 \cdot 7.1 + 1)^{\frac{1}{2}})

(2 (7.1) + 1)^{\frac{1}{2}} (7.1 - 1)^{2} = 145.07128 \dots

= ln (145.07128 \dots)

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