X+y-x²-xy=(x+y)-x(x+y)=(x+y)(1-x)
4ab²+5ab+a=4ab²+4ab+ab+a=4ab(b+1)+a(b+1)=(b+1)(4ab+a)=a(4b+1)(b+1)
(y-5)(y+11)=0
y-5=0 => y1=5
y+11=0 => y2=-1
t²+12t=0
t(t+12)=0
t1=0
t+12=0 => t2=-12
-x²+25=0
x²-25=0
(x-5)(x+5)=0
x-5=0 => x1=5
x+5=0 => x2=-5
![\left \{ {{x\ \textgreater \ -11} \atop {x \leq 2}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7Bx%5C+%5Ctextgreater+%5C+-11%7D+%5Catop+%7Bx+%5Cleq+2%7D%7D+%5Cright.+)
Значения х больше -11, но меньше или равно 2, поэтому ответ:
х∈(-11;2].
![20)log_{0,8}log_{2}log_{3}(x^{2} +3x-1)=0\\\\log_{2} log_{3} (x^{2}+3x-1)=0,8^{o}\\\\log_{2}logx_{3}(x^{2}+3x-1)=1\\\\log_{3}(x^{2}+3x-1)=2^{1}\\\\log_{3}(x^{2}+3x-1)=2\\\\x^{2}+3x-1=3^{2}\\\\x^{2}+3x-1=9\\\\x^{2}+3x-10=0\\\\x_{1}=2\\\\x_{2}=-5](https://tex.z-dn.net/?f=20%29log_%7B0%2C8%7Dlog_%7B2%7Dlog_%7B3%7D%28x%5E%7B2%7D%20%2B3x-1%29%3D0%5C%5C%5C%5Clog_%7B2%7D%20log_%7B3%7D%20%28x%5E%7B2%7D%2B3x-1%29%3D0%2C8%5E%7Bo%7D%5C%5C%5C%5Clog_%7B2%7Dlogx_%7B3%7D%28x%5E%7B2%7D%2B3x-1%29%3D1%5C%5C%5C%5Clog_%7B3%7D%28x%5E%7B2%7D%2B3x-1%29%3D2%5E%7B1%7D%5C%5C%5C%5Clog_%7B3%7D%28x%5E%7B2%7D%2B3x-1%29%3D2%5C%5C%5C%5Cx%5E%7B2%7D%2B3x-1%3D3%5E%7B2%7D%5C%5C%5C%5Cx%5E%7B2%7D%2B3x-1%3D9%5C%5C%5C%5Cx%5E%7B2%7D%2B3x-10%3D0%5C%5C%5C%5Cx_%7B1%7D%3D2%5C%5C%5C%5Cx_%7B2%7D%3D-5)
Проверкой убеждаемся, что оба корня подходят.
![23)3log_{4} x=2log_{3}x\\\\3log_{4}x -2\frac{log_{4}x}{log_{4}3}=0\\\\log_{4}x(3-\frac{2}{log_{4}3})=0\\\\log_{4}x=0\\\\x=4^{o}=1>0\\\\Otvet:1](https://tex.z-dn.net/?f=23%293log_%7B4%7D%20x%3D2log_%7B3%7Dx%5C%5C%5C%5C3log_%7B4%7Dx%20-2%5Cfrac%7Blog_%7B4%7Dx%7D%7Blog_%7B4%7D3%7D%3D0%5C%5C%5C%5Clog_%7B4%7Dx%283-%5Cfrac%7B2%7D%7Blog_%7B4%7D3%7D%29%3D0%5C%5C%5C%5Clog_%7B4%7Dx%3D0%5C%5C%5C%5Cx%3D4%5E%7Bo%7D%3D1%3E0%5C%5C%5C%5COtvet%3A1)
![24)3log_{9}x+2log_{x}9=5\\\\x>0;x\neq1\\\\3log_{9}x+\frac{2}{log_{9}x }-5=0\\\\log_{9}x=m\\\\3m+\frac{2}{m}-5=0\\\\\frac{3m^{2}-5m+2 }{m} =0\\\\\left \{ {{3m^{2}-5m+2=0 } \atop {m\neq0 }} \right.\\\\3m^{2}-5m+2=0\\\\D=(-5)^{2}-4*3*2=25-24=1\\\\m_{1}=\frac{5-1}{6} =\frac{2}{3}\\\\m_{2}=\frac{5+1}{6}=1\\\\1)log_{9}x=\frac{2}{3}\\\\x=9^{\frac{2}{3}}=\sqrt[3]{9^{2}}=\sqrt[3]{81}=3\sqrt[3]{3}\\\\2)log_{9}x=1\\\\x=9\\\\Otvet:9;3\sqrt[3]{3}](https://tex.z-dn.net/?f=24%293log_%7B9%7Dx%2B2log_%7Bx%7D9%3D5%5C%5C%5C%5Cx%3E0%3Bx%5Cneq1%5C%5C%5C%5C3log_%7B9%7Dx%2B%5Cfrac%7B2%7D%7Blog_%7B9%7Dx%20%7D-5%3D0%5C%5C%5C%5Clog_%7B9%7Dx%3Dm%5C%5C%5C%5C3m%2B%5Cfrac%7B2%7D%7Bm%7D-5%3D0%5C%5C%5C%5C%5Cfrac%7B3m%5E%7B2%7D-5m%2B2%20%7D%7Bm%7D%20%3D0%5C%5C%5C%5C%5Cleft%20%5C%7B%20%7B%7B3m%5E%7B2%7D-5m%2B2%3D0%20%7D%20%5Catop%20%7Bm%5Cneq0%20%7D%7D%20%5Cright.%5C%5C%5C%5C3m%5E%7B2%7D-5m%2B2%3D0%5C%5C%5C%5CD%3D%28-5%29%5E%7B2%7D-4%2A3%2A2%3D25-24%3D1%5C%5C%5C%5Cm_%7B1%7D%3D%5Cfrac%7B5-1%7D%7B6%7D%20%3D%5Cfrac%7B2%7D%7B3%7D%5C%5C%5C%5Cm_%7B2%7D%3D%5Cfrac%7B5%2B1%7D%7B6%7D%3D1%5C%5C%5C%5C1%29log_%7B9%7Dx%3D%5Cfrac%7B2%7D%7B3%7D%5C%5C%5C%5Cx%3D9%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%3D%5Csqrt%5B3%5D%7B9%5E%7B2%7D%7D%3D%5Csqrt%5B3%5D%7B81%7D%3D3%5Csqrt%5B3%5D%7B3%7D%5C%5C%5C%5C2%29log_%7B9%7Dx%3D1%5C%5C%5C%5Cx%3D9%5C%5C%5C%5COtvet%3A9%3B3%5Csqrt%5B3%5D%7B3%7D)