sin a = корень(1-(2/3)^2)=корень(5/9)=корень(5)/3
ctg a = cos a/ sin a= (2/3) / (3/ корень(5)) = 2/корень(5)
![\displaystyle 1)..9*81^{1-2x}=27^{2-x} \\ \\ 3^{2}* \frac{3^{4}}{3^{8x}}= \frac{3^{6}}{3^{3x}} \\ \\ \frac{3^{6}}{3^{8x}}= \frac{3^{6}}{3^{3x}} \\ \\3^{8x}=3^{3x} \\ 8x=3x \\ x=0](https://tex.z-dn.net/?f=%5Cdisplaystyle+1%29..9%2A81%5E%7B1-2x%7D%3D27%5E%7B2-x%7D+%5C%5C++%5C%5C+3%5E%7B2%7D%2A+%5Cfrac%7B3%5E%7B4%7D%7D%7B3%5E%7B8x%7D%7D%3D+%5Cfrac%7B3%5E%7B6%7D%7D%7B3%5E%7B3x%7D%7D++%5C%5C++%5C%5C++%5Cfrac%7B3%5E%7B6%7D%7D%7B3%5E%7B8x%7D%7D%3D+%5Cfrac%7B3%5E%7B6%7D%7D%7B3%5E%7B3x%7D%7D+%5C%5C++%5C%5C3%5E%7B8x%7D%3D3%5E%7B3x%7D+%5C%5C+8x%3D3x+%5C%5C+x%3D0++++++++)
Ответ: {0}
![\displaystyle 2)..2^{x-4}-2^{x}=120](https://tex.z-dn.net/?f=%5Cdisplaystyle+2%29..2%5E%7Bx-4%7D-2%5E%7Bx%7D%3D120)
так как уменьшаемое меньше вычитаемого при любом х, то данная разность не может быть положительным числом.
Ответ: ∅
![\displaystyle 3)..10*5^{x-1}+5^{x+1}=7 \\ \\ \frac{10*5^{x}}{5}+5*5^{x}=7 \\ \\ 10*5^{x}+25*5^{x}=35 \\ 35*5^{x}=35 \\ 5^{x}=1 \\ x=0](https://tex.z-dn.net/?f=%5Cdisplaystyle+3%29..10%2A5%5E%7Bx-1%7D%2B5%5E%7Bx%2B1%7D%3D7+%5C%5C++%5C%5C++%5Cfrac%7B10%2A5%5E%7Bx%7D%7D%7B5%7D%2B5%2A5%5E%7Bx%7D%3D7+%5C%5C++%5C%5C+10%2A5%5E%7Bx%7D%2B25%2A5%5E%7Bx%7D%3D35+%5C%5C+35%2A5%5E%7Bx%7D%3D35+%5C%5C+5%5E%7Bx%7D%3D1+%5C%5C+x%3D0+++)
Ответ: {0}
2 (4х+5)=3 (3х-2)+4 (2х-5)
8х+10=9х-6+8х-20
8х+10=17х-26
17х-8х=10+26
9х=36
х=36÷9
х=4
<span>-3х+9=-3+9
</span>-3х=-3+9-9
-3Х=-3
Х=1