Задание 1-4. Заранее спасибо.

Task/27552255
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1.
а) 5 +1 -2 =4 .
б) Log?(v5 - 1)(v5 - 1)Log?49 /Log?7 =Log?( (v5)? - 1?)Log?7?/Log?7 =
Log?(5 - 1) * 2Log?7/Log?7 =Log?2? * 2 =2*2=4 .
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2.
а) (1/9)? +8*(1/3)? - 9 =0 ?(1/3)?? +8*(1/3)? - 9 =0 ?( (1/3)? +9)( (1/3)? -1) =0 ?[ (1/3)? +9=0, (1/3)? — 9 =0 ?  (1/3)? =(1/3)??  ? x = -2.
* * * (1/3)? +9 > 9 ? 0 * * *
б) Log? x +4Log? x =9 ?Log? x +4Log??  x =9?Log? x +4*(1/2)Log? x =9?
Log? x +2Log? x=9?3Log? x=9?Log? x=3 ?x =27.
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3.
а) 2?(2? -3*2?+1) < 12 ?3*2? < 12 ?2? < 2?? x < 2. * * * 2 >1* * *
иначе x  ? ( -?, 2) .
б) (Log??? x)? -3*Log??? x — 4 ? 0 ?(Log? x)? +3*Log? x — 4 ? 0 ?
(Log? x)? +3*Log? x - 4 ? 0 ?((Log? x +4)(Log? x - 1)  ? 0 ?
-4 ? Log? x ? 1 ?2?? ? x? 2? ?  x  ? [ -  4, 2] .
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4.
Докажите числовое неравенство
(v3) ^ ( Log?  (v5 -2)? ) +(v2) ^ ( Log?(v5 -3)? ) =1.
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(v3) ^ ( Log?  (v5 -2)? ) +(v2) ^ ( Log?(v5 -3)? ) =
(v3) ^ (2*Log?|v5 -2| ) +(v2) ^ ( 2Log?|v5 -3| ) =
(v3)? ^ Log?(v5 -2) +(v2)? ^ Log?(3 -v5) =
(3) ^ Log?(v5 -2) ) +(2) ^ ( Log?(3 -v5 ) = (v5 -2) +(3 -v5 ) =1.