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rei741
@rei741
July 2022
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dasdasfa
C) log^2 (x+1) + log(1/2) (x+1)=6; ОДЗ: x>-1
log^2 (x+1) -log(2) (x+1)=6
log(2) (x+1)=t; t^2-t-6=0; D=1+24=25=5^2; t1=(1-5)/2=-2; t2=(1+5)/2=3
log(2) (x+1)=-2 ili log(2)(x+1)=3
x+1=2^(-2) x+1=2^3
x=-1+0,25 x=7
x=-0,75
Ответ -0,75; 7
d) lg^2(100x) +lg^2 (10x)=14+lg(1/x); x>0!
(lg100+lgx)^2 +(lg10+lgx)^2-14-lg(x^(-1))=0
(2+lgx)^2+1+2lgx+lg^2 x -14+lgx=0
4+4lgx+lg^2 x +1+2lgx+lg^2 x-14+lgx=0;
2lg^2 x+7lgx-9=0
lgx=t; 2t^2+7t-9=0; D=49+72=121=11^2; t1=(-7-11)/4=-9/2; t2=1
lgx=-9/2 ili lgx=1
x=10^(-4,5) x=10
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Answers & Comments
log^2 (x+1) -log(2) (x+1)=6
log(2) (x+1)=t; t^2-t-6=0; D=1+24=25=5^2; t1=(1-5)/2=-2; t2=(1+5)/2=3
log(2) (x+1)=-2 ili log(2)(x+1)=3
x+1=2^(-2) x+1=2^3
x=-1+0,25 x=7
x=-0,75
Ответ -0,75; 7
d) lg^2(100x) +lg^2 (10x)=14+lg(1/x); x>0!
(lg100+lgx)^2 +(lg10+lgx)^2-14-lg(x^(-1))=0
(2+lgx)^2+1+2lgx+lg^2 x -14+lgx=0
4+4lgx+lg^2 x +1+2lgx+lg^2 x-14+lgx=0;
2lg^2 x+7lgx-9=0
lgx=t; 2t^2+7t-9=0; D=49+72=121=11^2; t1=(-7-11)/4=-9/2; t2=1
lgx=-9/2 ili lgx=1
x=10^(-4,5) x=10