Question

Log3(x-1)+log3(x+1)=1 через одз

Answer 1

log3(x-1)+log3(x+1)=1. одз

log3(x+1)(x-1)=1. х-1>0

x²-1=3. х>1

x²=4. х+1>0

x=2. х>-1

х=-2 2-1>0 верно

2+1>0 верно

-2-1>0 неверно

-2+1>0 неверно

ответ:2

Answer 2

$x=2.$

Объяснение:

$log_{3} (x-1)+log_{3} (x+1)=1;\\ODZ:\left \{ {{x-10} \atop {x+10}} \right. =\left \{ {{x0+1} \atop {x0-1}} \right. =\left \{ {{x1} \atop {x-1}} \right. =x1=x$∈(1;+∞);

$log_{3} ((x-1)(x+1))=1;\\log_{3} (x^{2} -1)=1;\\x^{2} -1=3^{1} ;\\x^{2} -1=3;\\x^{2} =3+1;\\x^{2} =4;\\x=\pm2;\\x_{1} =2-PodxoditPoODZ;\\x_{2} =-2-NePodxoditPoODZ.$