3^x*(27+1)=2^x*(5*16-17)
3^x*28=2^x*63
(3/2)^x=63/28=9/4
x=2
8cos⁴x-8cos²x-cosx+1=
cosx=t
8t⁴-8t²-t+1=0
8t²(t²-1)-(t-1)=0
8t²(t-1)(t+1)-(t-1)=0
(t-1)(8t²(t+1-1))=0
t-1=0
t₁=1
8t³=0
t₂=0
cosx=1
x₁=2πn, n ∈ Z
cosx=0
x₂=π/2+πn, n ∈ Z
coszcos2zcos4zcos8z=1/16
16sinzcoszcos2zcos4zcos8z/2sinx=1
8sin2zcos2zcos4zcos8z=1
4sin4zcos4zcos8z=1
2sin8zcos8z=1
sin16z=1
16z=π/2+2πn
z=π/32+πn/8
4с(а-с)7с(а-с)=28с²(а-с)²
Logarifm označem naprimer x.
Potom nado 27na x = 3
27na x = 3na 3na x = 3 na 3x
3 = 3na 1
Polučajem uravnenie 3x=1, takže x = 1/3