1) log8(3x+8)=3
3x+8>0⇒3x>-8⇒x>-8/3
3x+8=512
3x=512-8
3x=504
x=168
2) log7 ( 6x-x^2 ) = log7 (33-8x)
6x-x²>0⇒x(6-x)>0⇒033-8x>0⇒8x<33⇒x<33/8<br>x∈(0;33/8)
6x-x²=33-8x
x²-14x+33=0
x1+x2=14 U x1*x2=33
x1=3
x2=11∉ОДЗ
3) log6 (5x+4) = 4 log6 (5)
5x+4>0⇒5x>-4⇒x>-0,8
5x+4=625
5x=621
x=124,2
4) log3-2x (1,96) = 2
3-2x>0⇒2x<3⇒x<1,5<br>3-2x≠1⇒2x≠2⇒x≠1
x∈(-∞;1) U (1;1,5)
(3-2x)²=1,96
9-12x+4x²-1,96=0
4x²-12x+7,04=0
x²-3x+1,76=0
D=9-7,04=1,96
x1=(3-1,4)/2=0,8
x2=(3+1,4)/2=2,2∉ОДЗ
5)(3+lgx)²-10(2+lgx)-21=0
9+6lgx+lg²x-20-10lgx-21=0
lg²x-4lgx-32=0
x>0
lgx=a
a²-4a-32=0
a1+a2=4 U a1*a2=-32
a1=-4⇒lgx=-4⇒x=0,0001
a2=8⇒lgx=8⇒x=100000000
0,0001*100000000=10000