6х-56-72х=-2х-8
6х-72х+2х=-8+56
-64х=48
х=-0,75
2x-3=2x+5-8
2x-2x=3+5-8
0=0
корней у уравнения безлич!!!
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Решение
1) 2^x = 5
log₂ (2^x) = log₂ 5
x = log₂ 5
2) 2^x - 1/4 = 0
2^x = 1/4
2^x = 2⁻²
x = - 2
A)
![4sin^3x=cos(x- \frac{ 5\pi }{2} ) \\ 4sin^3x=sinx \\ 4sin^3x-sinx=0 \\ sinx(4sin^2x-1)=0 \\ \\ sinx=0 \\ x= \pi k \\ \\ 4sin^2x-1=0 \\ 4sin^2x=1 \\ sin^2x= \frac{1}{4} \\ sinx=+- \frac{1}{2} \\ x=+- \frac{ \pi }{6}+ \pi k](https://tex.z-dn.net/?f=4sin%5E3x%3Dcos%28x-+%5Cfrac%7B+5%5Cpi+%7D%7B2%7D+%29+%5C%5C+4sin%5E3x%3Dsinx+%5C%5C+4sin%5E3x-sinx%3D0+%5C%5C+sinx%284sin%5E2x-1%29%3D0+%5C%5C++%5C%5C+sinx%3D0+%5C%5C+x%3D+%5Cpi+k+%5C%5C++%5C%5C+4sin%5E2x-1%3D0+%5C%5C+4sin%5E2x%3D1+%5C%5C+sin%5E2x%3D+%5Cfrac%7B1%7D%7B4%7D++%5C%5C+sinx%3D%2B-+%5Cfrac%7B1%7D%7B2%7D++%5C%5C+x%3D%2B-+%5Cfrac%7B+%5Cpi+%7D%7B6%7D%2B+%5Cpi+k+)
корнями из промежутка будут являться:
![\frac{11}{6} \pi ; 2 \pi ; \frac{13}{6} \pi](https://tex.z-dn.net/?f=+%5Cfrac%7B11%7D%7B6%7D++%5Cpi+%3B+2+%5Cpi+%3B++%5Cfrac%7B13%7D%7B6%7D++%5Cpi+)