1) lg(2x-5)= -1
ОДЗ: 2х-5>0
2x>5
x>2.5
2x-5=10⁻¹
2x-5=0.1
2x=5+0.1
2x=5.1
x=2.55 > 2.5
Ответ: 2,55
2) lg(2x+10)= 4lg2 + lg3
ОДЗ: 2х+10>0
2x> -10
x> -5
lg(2x+10)=lg2⁴ +lg3
lg(2x+10)=lg(16*3)
2x+10=48
2x=48-10
2x=38
x=19> -5
Ответ: 19
3) log(√3) X =2
ОДЗ: х>0
x=(√3)
x=3 >0
Ответ: 3
4) lg(x+53)=2
ОДЗ: х+53>0
x> -53
x+53=10²
x+53=100
x=100-53
x=47 > -53
Ответ: 47
![L(x)=f(a)+f'(a)(x-a)](https://tex.z-dn.net/?f=L%28x%29%3Df%28a%29%2Bf%27%28a%29%28x-a%29)
- уравнение касательной к функции
![f(x)](https://tex.z-dn.net/?f=f%28x%29)
в точке
![x=a](https://tex.z-dn.net/?f=x%3Da)
1)
![f'(x)=[x^6+4x^3-1]'=6x^5+12x^2\\\\ f'(-1)=-6+12=6\\\\ f(-1)=1-4-1=-4\\\\ L(x)=-4+6*(x-(-1))=-4+6(x+1) =-4+6x+6=\\\\=L(x)=6x+2](https://tex.z-dn.net/?f=f%27%28x%29%3D%5Bx%5E6%2B4x%5E3-1%5D%27%3D6x%5E5%2B12x%5E2%5C%5C%5C%5C+f%27%28-1%29%3D-6%2B12%3D6%5C%5C%5C%5C+f%28-1%29%3D1-4-1%3D-4%5C%5C%5C%5C+L%28x%29%3D-4%2B6%2A%28x-%28-1%29%29%3D-4%2B6%28x%2B1%29+%3D-4%2B6x%2B6%3D%5C%5C%5C%5C%3DL%28x%29%3D6x%2B2)
3)
![f(x)=\sqrt{5-4x}\\\\ f'(x)=\frac{(5-4x)'}{2\sqrt{5-4x}}=\frac{-4}{2\sqrt{5-4x}}=-\frac{2}{\sqrt{5-4x}}\\\\ f(1)=\sqrt{5-4}=1\\\\ f'(1)=-\frac{2}{1}=-2\\\\ L(x)=1+(-2)*(x-1)=1-2x+2=-2x+3\\\\ tg(\alpha)=-2\ \textless \ 0](https://tex.z-dn.net/?f=f%28x%29%3D%5Csqrt%7B5-4x%7D%5C%5C%5C%5C+f%27%28x%29%3D%5Cfrac%7B%285-4x%29%27%7D%7B2%5Csqrt%7B5-4x%7D%7D%3D%5Cfrac%7B-4%7D%7B2%5Csqrt%7B5-4x%7D%7D%3D-%5Cfrac%7B2%7D%7B%5Csqrt%7B5-4x%7D%7D%5C%5C%5C%5C+f%281%29%3D%5Csqrt%7B5-4%7D%3D1%5C%5C%5C%5C+f%27%281%29%3D-%5Cfrac%7B2%7D%7B1%7D%3D-2%5C%5C%5C%5C+L%28x%29%3D1%2B%28-2%29%2A%28x-1%29%3D1-2x%2B2%3D-2x%2B3%5C%5C%5C%5C+tg%28%5Calpha%29%3D-2%5C+%5Ctextless+%5C+0)
2) - скриншотами своего же решения ранее
тупой угол
Ответ : 3 по-моему , но лучше проверь
============== А1 ==============
![\frac{16x^6(a+2)^4}{12x^2(a+2)^5} = \frac{16}{12} \cdot x^{6-2}\cdot (a+2)^{4-5}= \frac{4}{3}\cdot x^ 4\cdot(a+2)^{-1}= \frac{4x^4}{3(a+2)}](https://tex.z-dn.net/?f=+%5Cfrac%7B16x%5E6%28a%2B2%29%5E4%7D%7B12x%5E2%28a%2B2%29%5E5%7D+%3D+%5Cfrac%7B16%7D%7B12%7D+%5Ccdot+x%5E%7B6-2%7D%5Ccdot+%28a%2B2%29%5E%7B4-5%7D%3D+%5Cfrac%7B4%7D%7B3%7D%5Ccdot+x%5E+4%5Ccdot%28a%2B2%29%5E%7B-1%7D%3D+%5Cfrac%7B4x%5E4%7D%7B3%28a%2B2%29%7D+)
Ответ: 1
============== А2 ==============
![\frac{8x}{3x-3y}- \frac{2x+6y}{3x-3y} = \frac{8x-(2x+6y)}{3x-3y} =\frac{8x-2x-6y}{3x-3y} =\frac{6x-6y}{3x-3y} =\frac{6(x-y)}{3(x-y)} =2](https://tex.z-dn.net/?f=+%5Cfrac%7B8x%7D%7B3x-3y%7D-+%5Cfrac%7B2x%2B6y%7D%7B3x-3y%7D++%3D+%5Cfrac%7B8x-%282x%2B6y%29%7D%7B3x-3y%7D+%3D%5Cfrac%7B8x-2x-6y%7D%7B3x-3y%7D+%3D%5Cfrac%7B6x-6y%7D%7B3x-3y%7D+%3D%5Cfrac%7B6%28x-y%29%7D%7B3%28x-y%29%7D+%3D2)
Ответ: 2
============== А3 ==============
![(2 \sqrt{5}-1 )(2 \sqrt{5}+1 )=(2 \sqrt{5})^2-1^2=4\cdot5-1=20-1=19](https://tex.z-dn.net/?f=%282+%5Csqrt%7B5%7D-1+%29%282+%5Csqrt%7B5%7D%2B1+%29%3D%282+%5Csqrt%7B5%7D%29%5E2-1%5E2%3D4%5Ccdot5-1%3D20-1%3D19)
Ответ: 2
============== А4 ==============
Оба утверждения верные.
Ответ: 3
============== B1 ==============
![\sqrt{54}\cdot \sqrt{6} = \sqrt{54\cdot 6} = \sqrt{324} =18](https://tex.z-dn.net/?f=+%5Csqrt%7B54%7D%5Ccdot+%5Csqrt%7B6%7D++%3D+%5Csqrt%7B54%5Ccdot+6%7D++%3D+%5Csqrt%7B324%7D+%3D18)