x₁=6; x₂=2
Пошаговое объяснение:
log₂(x+2)-log₀.₅(x+6)=1+log₂(x2+12)
-1 + logx+2/log2 + 1.4427logx+6 - logx²+12/log2 = 0
2.08137(-0.480453+0.693147log(x+2)+0.693147+log(x+6)-
-0.693147log(x²+12)=0
0.693147(-0.693147+1log(x+2)+1log(x+6)-log(x²+12))=0
-0.693147+log(x+2)+log(x+6)-log(x²+12)=0
log((x+2)(x+6)/x²+12) - 0.693147 = 0
log((x+2)(x+6)/x²+12) = 0.693147
(x+2)(x+6)/x²+12 = 2
(x+2)(x+6)=2(x²+12)
(x+2)(x+6)=2x²+24
-x²+8x-12=0
(x-6)(x-2)=0
x-6=0; x-2=0
x=6; x=2
x₁=6; x₂=2
Пошаговое объяснение:
log₂(x+2)-log₀.₅(x+6)=1+log₂(x2+12)
-1 + logx+2/log2 + 1.4427logx+6 - logx²+12/log2 = 0
2.08137(-0.480453+0.693147log(x+2)+0.693147+log(x+6)-
-0.693147log(x²+12)=0
0.693147(-0.693147+1log(x+2)+1log(x+6)-log(x²+12))=0
-0.693147+log(x+2)+log(x+6)-log(x²+12)=0
log((x+2)(x+6)/x²+12) - 0.693147 = 0
log((x+2)(x+6)/x²+12) = 0.693147
(x+2)(x+6)/x²+12 = 2
(x+2)(x+6)=2(x²+12)
(x+2)(x+6)=2x²+24
-x²+8x-12=0
(x-6)(x-2)=0
x-6=0; x-2=0
x=6; x=2