Log0.8 ( 3x^2 + x + 4 ) = log0.8 ( 17x+1 )
{17x+1>0⇒x>-1/17
{3x²+x+4>0⇒x∈R,
D=1-48=-47<0<br>x∈(-1/17;∞)
3x²+x+4=17x+1
3x²-16x+3=0
D=256-36=220
x1=(16-2√55)/6 U x2=(16+2√55(/2
log4 ( x-4 ) +log4 ( x+4 ) = log4 ( 3x+2)
{x-4>0⇒x>4
x+4>0⇒x>-4
{3x+2>0⇒x>-2/3
x∈(4;∞)
log(3)(x²-16)=log(4)(3x+2)
x²-16=3x+2
x²-3x-18=0
x1+x2=3 u x1*x2=-18
x1=-3 не удов усл
х2=6
log3 (3x+5) + log3 (2x-5) = log3 ( 10x -16)
{3x+5>0⇒x>-5/3
{2x-5>0⇒x>2,5
{10x-16>0⇒x>1,6
x∈(2,5;∞)
log(3)[(3x+5)(2x-5)]=log(3)(10x-16)
6x²-15x+10x-25=10x-16
6x²-15x-9=0
2x²-5x-3=0
D=25+24=49
x1=(5-7)/4=-0,5 не удов усл
х2=(5+7)/4=3