vereinfachen 9ln(cos^2(t))+9ln(1+tan^2(t))

Lösung

vereinfachen

9 ln (cos^{2} (t)) + 9 ln (1 + tan^{2} (t))

ln (sec^{18} (t) cos^{18} (t))

Schritte zur Lösung

9 ln (cos^{2} (t)) + 9 ln (1 + tan^{2} (t))

Wende die log Regel an:

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

9 ln (cos^{2} (t)) = ln (cos^{2} (t)^{9})

= ln (cos^{2} (t)^{9}) + 9 ln (tan^{2} (t) + 1)

Wende die log Regel an:

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

9 ln (tan^{2} (t) + 1) = ln ((tan^{2} (t) + 1)^{9})

= ln (cos^{2} (t)^{9}) + ln ((tan^{2} (t) + 1)^{9})

Wende die log Regel an:

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

ln (cos^{2} (t)^{9}) + ln ((1 + tan^{2} (t))^{9}) = ln (cos^{2} (t)^{9} (tan^{2} (t) + 1)^{9})

= ln (cos^{2} (t)^{9} (tan^{2} (t) + 1)^{9})

Vereinfache

cos^{2} (t)^{9} (1 + tan^{2} (t))^{9} : sec^{18} (t) cos^{18} (t)

= ln (sec^{18} (t) cos^{18} (t))

s im pl i f y lo g_{3} (5) + lo g_{3} (8) - lo g_{3} (2)

s im pl i f y 3 \cdot lo g_{10} (2) + 2 \cdot lo g_{10} (3)

s im pl i f y - 0.8 lo g_{2} (0.8) - 0.2 lo g_{2} (0.2)

s im pl i f y lo g_{10} (5 x + 4) - lo g_{10} (x)

s im pl i f y 2 lo g_{10} (x) + lo g_{10} (y)