![\frac{ log_{4}(16x^4)+11 }{ log_{4} ^{2}x-9 } \geq -1 \\ \\](https://tex.z-dn.net/?f=+%5Cfrac%7B+log_%7B4%7D%2816x%5E4%29%2B11+%7D%7B++log_%7B4%7D+%5E%7B2%7Dx-9+%7D++%5Cgeq+-1+%5C%5C++%5C%5C+)
одз
{x>0
{x≠64
{x≠1/64
![\frac{log_{4} 16+4 log_{4}x+11+ log_{4} ^{2}x-9 }{(log_{4}x-3)(log_{4}x+3)} \geq 0 \\ \\ \frac{log_{4} ^{2}x+4log_{4}x+4}{(log_{4}x- log_{4}64 )(log_{4}x- log_{4} \frac{1}{64} )} \geq 0 \\ \\ \frac{(log_{4}x-log_{4} \frac{1}{16} )^2}{(log_{4}x- log_{4}64 )(log_{4}x- log_{4} \frac{1}{64} )} \geq 0 \\ \\ \frac{(x- \frac{1}{16})^2 }{(x-64)(x- \frac{1}{64}) } \geq 0 \\ \\](https://tex.z-dn.net/?f=+%5Cfrac%7Blog_%7B4%7D+16%2B4+log_%7B4%7Dx%2B11%2B++log_%7B4%7D+%5E%7B2%7Dx-9++%7D%7B%28log_%7B4%7Dx-3%29%28log_%7B4%7Dx%2B3%29%7D+++%5Cgeq+0+%5C%5C++%5C%5C++%5Cfrac%7Blog_%7B4%7D+%5E%7B2%7Dx%2B4log_%7B4%7Dx%2B4%7D%7B%28log_%7B4%7Dx-+log_%7B4%7D64+%29%28log_%7B4%7Dx-+log_%7B4%7D+%5Cfrac%7B1%7D%7B64%7D++%29%7D++%5Cgeq+0+%5C%5C++%5C%5C++%5Cfrac%7B%28log_%7B4%7Dx-log_%7B4%7D+%5Cfrac%7B1%7D%7B16%7D+%29%5E2%7D%7B%28log_%7B4%7Dx-+log_%7B4%7D64+%29%28log_%7B4%7Dx-+log_%7B4%7D+%5Cfrac%7B1%7D%7B64%7D++%29%7D++%5Cgeq+0+%5C%5C++%5C%5C++%5Cfrac%7B%28x-+%5Cfrac%7B1%7D%7B16%7D%29%5E2+%7D%7B%28x-64%29%28x-+%5Cfrac%7B1%7D%7B64%7D%29+%7D++%5Cgeq+0+%5C%5C++%5C%5C+)
+++++(1/64)-----------[1/16]---------(64)
x∈(-∞;1/64)U{1/16}U(64;+∞)
с учетом одз получаем ответ
x∈(0;1/64)U{1/16}U(64;+∞)
1) 1,8a¹⁵b⁷
2) -3,2c⁵d⁵
3) -1,4x³t⁶
4) -b¹⁴
5) -2,1a⁷t⁹
6) -b¹¹c⁸
при умножении одинаковых переменных степени складываем
<em>1)</em><em><u>14a*6b</u></em> при a=2,b=3
14*2*6*3=28*18=504
<em>Ответ: 504</em>
<em>2)</em><u><em>25m*3n</em></u> при m=8,n=1
25*8*3*1=25*24=600
<em>Ответ: 600</em>
3)<u><em>5x + 8x - 3x</em></u> = 13x-3x=10x при x=17
17*10=170
<em>Ответ: 170</em>
<em>4) <u>16y - y + 5y</u></em> = 15y+5y=20y при y=23
23*20=460
<em>Ответ: 460</em>