Решить ур-ие

1) log3 (4+3x) = 2

2) log3 (4-x) = 3

3) cos x+2cos 2x=1

4) cos 2x=2cos x-1

1) log₃ (4+3x) = 2

log₃ (4+3x) = log₃3²

4+3x=9

3x=9-4

x=5/3

2) log₃ (4-x) = 3

log₃ (4-x) = log₃3³

4-x=27

-x=27/4

x=-27/4

3) cosx+2cos2x=1

cos2x=2cos²x-1

cosx+2 (2cos²x-1) = 1

cosx+4cos²x-2-1=0

4cos²x+cosx-3=0

cosx=t

4t²+t-3=0

D=1²-4*4 * (-3) = 1+48=49

t = (-1-7) / 8=-1 t = (-1+7) / 8=3/4

cosx=-1 cosx=3/4

x=π+2πn, n∈Z

4) cos2x=2cosx-1

cos2x=2cos²x-1

2cos²x-1=2cosx-1

2cos²x-2cosx=-1+1

2cosx (cosx-1) = 0

cosx=0 cosx-1=0

x=π/2+πn, n∈Z cosx=1

x=2πn, n∈Z

Log3 (4+3x) = 2log3 (3) = > 4+3x=9 = >x=5/3 = > 2) log3 (4-x) = 3log3 (3) = > 4-x=27 = > x=-23