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а)
![2^{x+1}-2^x=112 \ 2^x(2-1)=112 \ 2^x=112 \ x=log_2112=log_2(16*7)=log_22^4+log_27=4+log_27 2^{x+1}-2^x=112 \ 2^x(2-1)=112 \ 2^x=112 \ x=log_2112=log_2(16*7)=log_22^4+log_27=4+log_27](https://tex.z-dn.net/?f=2%5E%7Bx%2B1%7D-2%5Ex%3D112+%5C+2%5Ex%282-1%29%3D112+%5C+2%5Ex%3D112+%5C+x%3Dlog_2112%3Dlog_2%2816%2A7%29%3Dlog_22%5E4%2Blog_27%3D4%2Blog_27)
x = 4 + log₂7
b) 2 cos²x - 3sin x - 3 = 0
2(1 - sin²x) - 3sin x - 3 = 0
2 - 2sin²x - 3sin x - 3 = 0 | * (-1)
2 sin²x + 3 sin x + 1 = 0
D = 9 - 4*2*1 = 1
1) sin x = (-3 + 1)/4 = -1/2
![x_1=- frac{ pi }{6} + 2 pi n; x_2 = - frac{5 pi }{6} +2 pi k x_1=- frac{ pi }{6} + 2 pi n; x_2 = - frac{5 pi }{6} +2 pi k](https://tex.z-dn.net/?f=x_1%3D-+frac%7B+pi+%7D%7B6%7D+%2B+2+pi+n%3B+x_2+%3D+-+frac%7B5+pi+%7D%7B6%7D+%2B2+pi+k)
2) sin x = (-3 - 1)/4 = -1
![x_3=- frac{ pi }{2} + 2 pi n x_3=- frac{ pi }{2} + 2 pi n](https://tex.z-dn.net/?f=x_3%3D-+frac%7B+pi+%7D%7B2%7D+%2B+2+pi+n)
Ответ:![x_1=- frac{ pi }{6} + 2 pi n; x_2 = - frac{5 pi }{6} +2 pi k x_1=- frac{ pi }{6} + 2 pi n; x_2 = - frac{5 pi }{6} +2 pi k](https://tex.z-dn.net/?f=x_1%3D-+frac%7B+pi+%7D%7B6%7D+%2B+2+pi+n%3B+x_2+%3D+-+frac%7B5+pi+%7D%7B6%7D+%2B2+pi+k)
; n,k,m ∈ Z
x = 4 + log₂7
b) 2 cos²x - 3sin x - 3 = 0
2(1 - sin²x) - 3sin x - 3 = 0
2 - 2sin²x - 3sin x - 3 = 0 | * (-1)
2 sin²x + 3 sin x + 1 = 0
D = 9 - 4*2*1 = 1
1) sin x = (-3 + 1)/4 = -1/2
2) sin x = (-3 - 1)/4 = -1
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