3^(x+1)+ 18/3^x -29 =0 ;
3*3^x +18/3^x -29 =0 ;
3t +18/t -29 =0 ;
3t² -29t +18 =0 ;
t₁=(29 -25)/6 =2/3 ;
t₂ =(29 +25)/6 =9.
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3^x =2/3 ;
x ₁=Loq (3) 2 -1.
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3^x =9 ;
x =2.
ответ : Loq (3) 2 -1 ; 2.
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(Loq(2) (x-1))² - Loq(1/2) (x-1)) > 2 ;
(Loq(2) (x-1))² + Loq(2) (x-1) - 2> 0 ; * * * t =Loq(2) (x-1) * * *
(Loq(2) (x-1) +2)(Loq(2) (x-1) -1) > 0 ;
[ Loq(2) (x-1) < - 2 ; Loq(2) (x-1) >1 . [ 02.
[ 1< x <5/4 ; x>3 .
ответ : x ∈(1;5/4) U (3 ;∞) .