vereinfachen ln(1+0.5^4+20.5^2)+ln(1+0.5^4-20.5^2)

Lösung

vereinfachen

ln (1 + 0. 5^{4} + 2 \cdot 0. 5^{2}) + ln (1 + 0. 5^{4} - 2 \cdot 0. 5^{2})

ln (0.87890625)

Dezimale

- 0.12907 \dots

Schritte zur Lösung

ln (1 + 0. 5^{4} + 2 \cdot 0. 5^{2}) + ln (1 + 0. 5^{4} - 2 \cdot 0. 5^{2})

Wende die log Regel an:

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

ln (1 + 0. 5^{4} + 2 \cdot 0. 5^{2}) + ln (1 + 0. 5^{4} - 2 \cdot 0. 5^{2}) = ln ((1 + 2 \cdot 0. 5^{2} + 0. 5^{4}) (1 + 0. 5^{4} - 2 \cdot 0. 5^{2}))

= ln ((1 + 2 \cdot 0. 5^{2} + 0. 5^{4}) (1 + 0. 5^{4} - 2 \cdot 0. 5^{2}))

(1 + 0. 5^{4} + 2 \cdot 0. 5^{2}) (1 + 0. 5^{4} - 2 \cdot 0. 5^{2}) = 0.87890625

= ln (0.87890625)

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