2) 5^(5x+1) = 25^(2x)
5^(5x+1)=5^(4x)
5x+1=4x
x=-1
3) sin^2 x + cos^2 x=1
(1/3)^2 + cos^2 x =1
cos^2 x=1-1/9
cosx= 2√2/3
x= +- arccos 2√2/3 + 2πn
4)㏒2 (x+1)=2
log2 (x+1) = log2 2^2
x+1=4
x=3
5)cos2x= -1/2
2x= 2π/3 + 2πn
x= π/3 + πn
6) x-6= √(8-x)
(x-6)^2= 8-x
x^2 - 11x +28=0
D= 3^2
x=7; x=4; v otvet vhodit tolko x=7
7) 15^(√5 -3) × 15^(5-√5)=15^(√5 -3)+(5-√5)=15^2= 225.
8)3×∛49× 6^√49= 3×7^(2/3) ×7^(2/6)= 3×7=21
9)log2 80 - log2 2,5= log2 (80/2,5)= log2 32= log2 2^5=5.
10) f(-1)-? f(x)= x^3 -3x^2 -4
f(-1)= (-1)^3 - 3(-1)^2 -4=-1-3-4=-8
11) f(x)= 2x+1/3x-1
(2x+1)=0
x=-1/2
3x-1≠0
x=1/3
12) y= x^3 -12x+2 [-4;0]
1) находим производную функции
y'=(x^3 -12x+2)'= 3x^2-12
3x^2-12=0
x=2 x=-2
х=-2 входит в наш отрезок[-4;0]
y(0)=2
y(-2)= 18
y(-4)= -14
ymin=y(-4)=-14
17)
(x^3 +4x)dx= 2x^2 + x^4/4
=36.