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

Question

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

Answer 1

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<br>{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