1)2^5*2^-4=2
2) 5^-6*5=1/3125
3) 3^6: 3^7=1/3
4) 7: 7^-1 =49
5)(2^-2) ^3=1/64
6) ((1/3) ^-1) ^-4
=1/81
7) -13*26^-1=-1/2
8) -6*3^-3=-2/9
9) 81*3^-5=1/3
10) 16*(2^-3) ^2=1/4
11)32^-2*4^4=1/4
12) 27^-3: 9^-4=1/3
13) (1/7) ^-8*(1/7) ^7
=7
14) (1/3) ^12*)(1/3) ^-15=27
15)4^-7: 4^-10=64
16) (1/5)^-9: (1/5) ^-9=1
17) (0.01^-2) ^4 =10000000000000000
18) ((1/7) ^-2) ^0=1
19) (1/9) ^-2+0.1^-2
=181
20)14^-1-7^-2
=1/14-1/49=(7-2)/98=5/98
21) 5^-6*5^8: 125
=1/5
22)36^-1*(1/6) ^-4
=36
23) 7^-6*7^-8/(-7) ^-13
=-1/7
24) 81^-5*9^-8/27^-11=1/27
Ответ: 4.
49/15=3,2(6); 3,2<4
52/15=3,4(6); 3,4<4
58/15=3,8(6); 3,8<4
71/15=4,7(3); 4<4,7<5
А)уне равно 2;б)х не равно 0; -7
![\dfrac{2}{\log_{2}x}+\dfrac{5}{\log^{2}_{2}x-\log_{2}x^{3}}\leq \dfrac{\log_{2}x}{\log_{2}\left(\dfrac{x}{8}\right)}](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7B%5Clog_%7B2%7Dx%7D%2B%5Cdfrac%7B5%7D%7B%5Clog%5E%7B2%7D_%7B2%7Dx-%5Clog_%7B2%7Dx%5E%7B3%7D%7D%5Cleq+%5Cdfrac%7B%5Clog_%7B2%7Dx%7D%7B%5Clog_%7B2%7D%5Cleft%28%5Cdfrac%7Bx%7D%7B8%7D%5Cright%29%7D)
<u><em>Заметим, что можно выполнить некие равносильные преобразования</em></u>
![\log_{2}x^{3}\Leftrightarrow 3\log_{2}x;~\log_{2}\left(\dfrac{x}{8}\right)\Leftrightarrow\log_{2}x-\log_{2}8=\log_{2}x-3](https://tex.z-dn.net/?f=%5Clog_%7B2%7Dx%5E%7B3%7D%5CLeftrightarrow+3%5Clog_%7B2%7Dx%3B~%5Clog_%7B2%7D%5Cleft%28%5Cdfrac%7Bx%7D%7B8%7D%5Cright%29%5CLeftrightarrow%5Clog_%7B2%7Dx-%5Clog_%7B2%7D8%3D%5Clog_%7B2%7Dx-3)
Тогда, пусть ![\log_{2}x=t](https://tex.z-dn.net/?f=%5Clog_%7B2%7Dx%3Dt)
![\dfrac{2}{t}+\dfrac{5}{t^2-3t}\leq \dfrac{t}{t-3}\bigskip\\\dfrac{2(t-3)+5-t^2}{t(t-3)}\leq 0~|:(-1)\bigskip\\\dfrac{t^2-2t+6-t}{t(t-3)}\geq 0\bigskip\\\dfrac{\left(t-1\right)^2}{t(t-3)}\geq 0\Leftrightarrow t\in\left(-\infty;0\right)\cup\left\{1\right\}\cup\left(3;+\infty\right)](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7Bt%7D%2B%5Cdfrac%7B5%7D%7Bt%5E2-3t%7D%5Cleq+%5Cdfrac%7Bt%7D%7Bt-3%7D%5Cbigskip%5C%5C%5Cdfrac%7B2%28t-3%29%2B5-t%5E2%7D%7Bt%28t-3%29%7D%5Cleq+0~%7C%3A%28-1%29%5Cbigskip%5C%5C%5Cdfrac%7Bt%5E2-2t%2B6-t%7D%7Bt%28t-3%29%7D%5Cgeq+0%5Cbigskip%5C%5C%5Cdfrac%7B%5Cleft%28t-1%5Cright%29%5E2%7D%7Bt%28t-3%29%7D%5Cgeq+0%5CLeftrightarrow+t%5Cin%5Cleft%28-%5Cinfty%3B0%5Cright%29%5Ccup%5Cleft%5C%7B1%5Cright%5C%7D%5Ccup%5Cleft%283%3B%2B%5Cinfty%5Cright%29)
<u><em>Перейдём обратно к иксу</em></u>
![\log_{2}x\in\left(-\infty;0\right)\cup\left\{1\right\}\cup\left(3;+\infty\right)\Leftrightarrow x\in\left(0;1\right)\cup\{2\}\cup\left(8;+\infty\right)](https://tex.z-dn.net/?f=%5Clog_%7B2%7Dx%5Cin%5Cleft%28-%5Cinfty%3B0%5Cright%29%5Ccup%5Cleft%5C%7B1%5Cright%5C%7D%5Ccup%5Cleft%283%3B%2B%5Cinfty%5Cright%29%5CLeftrightarrow+x%5Cin%5Cleft%280%3B1%5Cright%29%5Ccup%5C%7B2%5C%7D%5Ccup%5Cleft%288%3B%2B%5Cinfty%5Cright%29)
<u><em>Ответ.</em></u> ![x\in\left(0;1\right)\cup\{2\}\cup\left(8;+\infty\right)](https://tex.z-dn.net/?f=x%5Cin%5Cleft%280%3B1%5Cright%29%5Ccup%5C%7B2%5C%7D%5Ccup%5Cleft%288%3B%2B%5Cinfty%5Cright%29)
Ответ:
45
на 2 моркови больше
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