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Beliebt Algebra >

vereinfachen 5ln(cos^2(t))+5ln(1+tan^2(t))

Lösung

vereinfachen

5 ln (cos^{2} (t)) + 5 ln (1 + tan^{2} (t))

Lösung

ln (sec^{10} (t) cos^{10} (t))

Schritte zur Lösung

5 ln (cos^{2} (t)) + 5 ln (1 + tan^{2} (t))

Wende die log Regel an:

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

5 ln (cos^{2} (t)) = ln (cos^{2} (t)^{5})

= ln (cos^{2} (t)^{5}) + 5 ln (tan^{2} (t) + 1)

Wende die log Regel an:

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

5 ln (tan^{2} (t) + 1) = ln ((tan^{2} (t) + 1)^{5})

= ln (cos^{2} (t)^{5}) + ln ((tan^{2} (t) + 1)^{5})

Wende die log Regel an:

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

ln (cos^{2} (t)^{5}) + ln ((1 + tan^{2} (t))^{5}) = ln (cos^{2} (t)^{5} (tan^{2} (t) + 1)^{5})

= ln (cos^{2} (t)^{5} (tan^{2} (t) + 1)^{5})

Vereinfache

cos^{2} (t)^{5} (1 + tan^{2} (t))^{5} : sec^{10} (t) cos^{10} (t)

= ln (sec^{10} (t) cos^{10} (t))

Beliebte Beispiele

zusammenfügen 3/2 ln(3)

j o in \frac{3}{2} ln (3)

vereinfachen-log_{10}(2.5*10^{-7})

s im pl i f y - lo g_{10} (2.5 \cdot 1 0^{- 7})

vereinfachen log_{10}((xz^2)/y)

s im pl i f y lo g_{10} (\frac{x z ^{2}}{y})

erweitern ln(x/(sqrt(x^2+1)))

e x p an d ln (\frac{x}{x ^{2} + 1})

erweitern ln((ex^2)/y)

e x p an d ln (\frac{e x ^{2}}{y})