Question

Помогите решить логарифмические уравнения)

Answer 1

1) log3(x–2) + log3(x+6)=2
log3(x–2)(x+6)=log3 9
(x–2)(x+6)=9
x^2+6x–2x–12–9=0
x^2+4x–21=0
Д=/16–4*1*(-21)=/100=10
х1=(-4+10)/2=3
х2=(-4-10)/2=-7

2) lg(x–1) + lg(x+1) = 0
lg(x–1)(x+1)=lg1
(x–1)(x+1)=1
x^2–1=1
x^2=2
x=/2

3) lg(3x–1) – lg(x+5)=lg5

3x–1
lg -------- = lg5
x+5

3x–1
--------- = 5
x+5
3x–1=5x+25
–2x=26
x=–13

4) 1/2 lg(x^2–4x–1) = lg(8x) – lg(4x)
1/2 lg(x^2–4x–1) = lg(8x/4x)
1/2* (x^2–4x–1) = 2 |*2
x^2–4x–1 = 4
x^2–4x–5=0
Д=/16–4*1*(-5)=/36=6
х1=(4+6)/2=5
х2=(4–6)/2 = –1