Решить: 1. log₃/₂ (1/2x) = 1 2. log₄ (9x²+1/4) = - 1/2 3. log₄ (7x-3) - log₄ (8 х-8) = 1/2 4. ln (2-x) = ln 5 - ln (x+4)

1

1/2x=3/2

x=3/2:1/2

x=3

2

9x²+1/4=1/2

9x²=1/2-1/4

9x²=1/4

x²=1/36

x=-1/6 U x=1/6

3

{7x-3>0⇒x>3/7

{8x-8>0⇒x>1

x∈ (1; ∞)

log (x) [ (7x-3) / (8x-8 (]=1/2

(7x-3) / (8x-8) = 2

7x-3=16x-16

16x-7x=-3+16

9x=13

x=13/9

4

{2-x>0⇒x<2

{x+4>0⇒x>-4

x∈ (-4; 2)

ln (2-x) = ln[5 / (x+4) ]

2-x=5 / (x+4)

(2-x) (x+4) = 5

5-2x-8+x²+4x=0

x²+2x-3=0

x1+x2=-2 U x1*x2=-3

x1=-3 U x2=1