Не уверенна конечно, но думаю, что так: 1(5/7)-7/13
Log(по основанию 2)(х-1)<3
0<x-1<8, -1< x<9
x1=5*pi/6+2pi*k, k∈Z
x2=7*pi/6+2pi*k,k∉Z
в интервал (-1;9) входят x=5*pi/6, x=7*pi/6,x= 17*pi/6,
Пусть s км - длина всего пути
![v_{cp}=\dfrac{s_1+s_2+s_3}{t_1+t_2+t_3}](https://tex.z-dn.net/?f=v_%7Bcp%7D%3D%5Cdfrac%7Bs_1%2Bs_2%2Bs_3%7D%7Bt_1%2Bt_2%2Bt_3%7D)
(км/ч)
![t_1=\dfrac{ \frac{1}{3}s }{100}=\dfrac{s}{300}](https://tex.z-dn.net/?f=t_1%3D%5Cdfrac%7B+%5Cfrac%7B1%7D%7B3%7Ds+%7D%7B100%7D%3D%5Cdfrac%7Bs%7D%7B300%7D)
(ч)
![t_2=\dfrac{ \frac{1}{3}s }{75}=\dfrac{s}{225}](https://tex.z-dn.net/?f=t_2%3D%5Cdfrac%7B+%5Cfrac%7B1%7D%7B3%7Ds+%7D%7B75%7D%3D%5Cdfrac%7Bs%7D%7B225%7D)
(ч)
![t_3=\dfrac{ \frac{1}{3}s }{60}=\dfrac{s}{180}](https://tex.z-dn.net/?f=t_3%3D%5Cdfrac%7B+%5Cfrac%7B1%7D%7B3%7Ds+%7D%7B60%7D%3D%5Cdfrac%7Bs%7D%7B180%7D)
(ч)
![t_1+t_2+t_3=t_1=\frac{s}{300}+\frac{s}{225}+\frac{s}{180}= \frac{s}{15} ( \frac{1}{20}+ \frac{1}{15}+ \frac{1}{12})= \frac{s}{15} * \frac{12}{60} = \frac{s}{75}](https://tex.z-dn.net/?f=t_1%2Bt_2%2Bt_3%3Dt_1%3D%5Cfrac%7Bs%7D%7B300%7D%2B%5Cfrac%7Bs%7D%7B225%7D%2B%5Cfrac%7Bs%7D%7B180%7D%3D+%5Cfrac%7Bs%7D%7B15%7D+%28+%5Cfrac%7B1%7D%7B20%7D%2B+%5Cfrac%7B1%7D%7B15%7D%2B+%5Cfrac%7B1%7D%7B12%7D%29%3D+%5Cfrac%7Bs%7D%7B15%7D+%2A+%5Cfrac%7B12%7D%7B60%7D+%3D+%5Cfrac%7Bs%7D%7B75%7D+)
(ч)
![v_{cp}=\dfrac{s_1+s_2+s_3}{t_1+t_2+t_3}=\dfrac{ \frac{1}{3} s+\frac{1}{3} s+\frac{1}{3} s}{ \frac{s}{75} }=\dfrac{75*s}{s}=75](https://tex.z-dn.net/?f=v_%7Bcp%7D%3D%5Cdfrac%7Bs_1%2Bs_2%2Bs_3%7D%7Bt_1%2Bt_2%2Bt_3%7D%3D%5Cdfrac%7B+%5Cfrac%7B1%7D%7B3%7D+s%2B%5Cfrac%7B1%7D%7B3%7D+s%2B%5Cfrac%7B1%7D%7B3%7D+s%7D%7B+%5Cfrac%7Bs%7D%7B75%7D+%7D%3D%5Cdfrac%7B75%2As%7D%7Bs%7D%3D75)
(км/ч)
Ответ: 75 км/ч.
2sin3x=-1
sin3x=-1/2
3x=-п/6+2пn,n€z
x=-п/18+2пn/3,n€z
3x=7п/6+2пn,n€z
x=7п/18+2пn/3,n€z
-п≤-п/18+2пn/3≤п
-п+п/18≤2пn/3≤п+п/18 |:п
-1+1/18≤2n/3≤1+1/18
-17/18≤2n/3≤19/18 |*3
-17/6≤2n≤19/6 |:2
-17/12≤n≤19/12
при n=0 x=-п/18
при n=-1 x=-п/18-2п/3=-п/18-12п/18=-13п/18
при n=1 x= -п/18+2п/3=-п/18+12п/18=11п/18
-п≤7п/18+2пn/3≤п |:п
-1≤7/18+2n/3≤1
-1-7/18≤2n/3≤1-7/18
-25/18≤2n/3≤11/18 |*3
-25/6≤2n≤11/6 |:2
-25/12≤n≤11/12
при n=-2 x=7п/18-4п/3=7п/18-24п/18=-17п/18
при n=-1 x=7п/18-2п/3=7п/18-12п/18=-5п/18
при n=0 x=7п/18