9^x * (1/3)^(2-3x) =√27^x * ∛(81^(x+3) ;
3^(2x)*(3)^(-1(2-3x)) =3^(3x/2) *3^(4(x+3)/3);
3^(2x +3x-2) =3^(3x/2 +4(x+3)/3) ;
2x +3x-2 =3x/2 +4(x+3)/3 ;
5x-2 = 3*3x+8(x+3)/6 ;
6(5x -2) =9x +8x +24 ;
13x =36 ⇒ x =36/3.
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2^(1-x) -2^(3+x) -15=0;
2*2^(-x) -(2^3)*2^x -15 =0 ;
2/2^x -8*2^x -15 =0 ;
замена переменной t=2^x >0 ;
2/t -8t -15 =0 ;
8t²+15t -2 =0 ;
t = (-15 +√(15² -4*4(-2) /16 ;
t ₁ = (-15 - 17)/16 = -2 < 0 (не решение)
t₂ = (-15 + 17)/16 =1/8 ⇒ 2^x =1/8 ⇔ 2^x =2^(-3) ⇒ x =-3.