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Beliebt Algebra >

vereinfachen 2ln(cos^2(t))+2ln(1+tan^2(t))

Lösung

vereinfachen

2 ln (cos^{2} (t)) + 2 ln (1 + tan^{2} (t))

Lösung

ln (sec^{4} (t) cos^{4} (t))

Schritte zur Lösung

2 ln (cos^{2} (t)) + 2 ln (1 + tan^{2} (t))

Wende die log Regel an:

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

2 ln (cos^{2} (t)) = ln (cos^{2} (t)^{2})

= ln (cos^{2} (t)^{2}) + 2 ln (tan^{2} (t) + 1)

Wende die log Regel an:

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

2 ln (tan^{2} (t) + 1) = ln ((tan^{2} (t) + 1)^{2})

= ln (cos^{2} (t)^{2}) + ln ((tan^{2} (t) + 1)^{2})

Wende die log Regel an:

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

ln (cos^{2} (t)^{2}) + ln ((1 + tan^{2} (t))^{2}) = ln (cos^{2} (t)^{2} (tan^{2} (t) + 1)^{2})

= ln (cos^{2} (t)^{2} (tan^{2} (t) + 1)^{2})

Vereinfache

cos^{2} (t)^{2} (1 + tan^{2} (t))^{2} : sec^{4} (t) cos^{4} (t)

= ln (sec^{4} (t) cos^{4} (t))

Beliebte Beispiele

vereinfachen ln(5)+1/2 ln(16)

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vereinfachen 5log_{a}(a)-log_{a}(a^4)+log_{a}(a^{-2})

s im pl i f y 5 lo g_{a} (a) - lo g_{a} (a^{4}) + lo g_{a} (a^{- 2})

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