Ответы и объяснения

2014-01-18T11:23:10+00:00
1) ОДЗ: x>0
   log₂x +  \frac{ log_{2}x }{ log_{2}4 } +  \frac{ log_{2}x }{ log_{2}8 } = 11
log₂x +  \frac{ log_{2}x }{2}+ \frac{ log_{2}x }{3}  = 11
6log₂x + 3log₂x + 2log₂x = 66
11log₂x = 66
log₂x = 6
x = 64
Ответ: 64
2) ОДЗ: x>0
log₆₄x + log₈x = 0.5
 \frac{ log_{2}x }{6} +  \frac{ log_{2}x }{3} = 0.5
log₂x + 2log₂x = 3
3log₂x = 3
log₂x = 1
x = 2
Ответ: 2
3) ОДЗ: x>0
 \frac{ log_{3}x }{4} +  \frac{ log_{3}x }{2}+ log_{3}x = 3.5
log₃x + 2log₃x + 4log₃x = 14
7log₃x = 14
log₃x = 2
x = 9
Ответ: 9