1) log₃x * (5 - 2log₃x) = 3
5log₃x - 2log₃²x = 3
2log₃²x - 5log₃x + 3 = 0
log₃x = t
2t² - 5t + 3 =0
t₁ = 1
t₂ =
log₃x = 1
x = 3log₃x =
x = Ответ: 3 ;
2) log₂²x + 3log₁/₂x + 2 =0
log₂²x + 3*
+ 2 = 0
log₂²x - 3log₂x + 2 =0
log₂x = t
t² - 3t + 2 =0
t₁ = 1
t₂ = 2
log₂x = 1
x = 2log₂x = 2
x = 4Ответ: 2; 4
3) (1/2log₃x - 6 )*log₉x = 4(2-log₉x)
(1/2log₃x - 6) *
log₃x = t
t² - 12t = 32 - 8t
t² - 4t - 32 = 0
D₁ = 4+32=36
t₁ = 8
t₂ = -4
log₃x = 8
x = log₃x = -4
x = 4) log₂x * log₃x = 4log₃2
log₃x = 2log₃2 log₃x = -2log₃2
log₃x = log₃4 log₃x = log₃
x=4 x = 5) lg²x + 4 = 2*2*lgx
lg²x - 4lgx + 4 = 0
lgx = t
t² - 4t + 4=0
D₁ = 4-4=0
t = 2
lgx = 2
x = 100
1) =x²-2+1
2) =9a²-6ab+b²
3) =25z²+10zt+t²
4) =25x²+10zt+t²
5) =36m²-48mn+16n²
6) =a²-8a+16
7) =0.04a²+0.4ab+b²
8) =a²-4a+4
9) =b²+6b+9
10) =n²-8n+16
11) =(x+y)²
12) =(b-3)²
13) =(2m+1)²
14) =(4-c)²
15) =(3a-4b)²
16) =(2c+3)²
17) =(5x+1)²
18) =(9x-y)²
19) =m²-4mn+4n²=(m-2n)²
20) =100a²+20ab+b2=(10a+b)²
A) 125^(1.5) · 25^(-3/4) = 5^(3 · 1.5) · 5^ (2 · (-3/4) =
= 5^(4.5) · 5^(-1.5) = 5^(4.5 - 1.5) = 5³ = 125
Б) 2^(1.25) · 16^(1/16) = 2^(1.25) · 2^(4 · 1/16) =
= 2^(1.25 + 0.25) = 2^1.5 = 2√2