1. Решить неравенство: log2(x-2)≤ 3-log2x
log₂(x-2)≤3-log₂x
log₂(x-2)≤log₂8-log₂x
log₂(x-2)≤log₂(8/x)
x-2≤8/x
((x-4)(x+2))/x≤0
(-∞;-2]∨(0;4]
ОДЗ
х>0, х>2
Ответ:(2;4]
Copyright © 2024 SCHOLAR.TIPS - All rights reserved.
Answers & Comments
Verified answer
log₂(x-2)≤3-log₂x
log₂(x-2)≤log₂8-log₂x
log₂(x-2)≤log₂(8/x)
x-2≤8/x
((x-4)(x+2))/x≤0
(-∞;-2]∨(0;4]
ОДЗ
х>0, х>2
Ответ:(2;4]