5. 9^(x² -3x) =81^(-5/8) ;
9^(x² -3x) =9^(-5/4) ;
x² -3x = - 5/4 ;
4x² - 12x +5 = 0 ;
x₁ =(6 -√(6² - 4*5))/4 = 1/2;
x₂ =(6+√(6² - 4*5))/4 = 5/2 .
min(x) =1/2.
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6. (1/3)^(x²-9x+10) = 1/9 ;
(1/3)^(x²-9x+10) = (1/3)² ;
x²-9x+10 =2 ;
x²-9x+8 =0 ; * * * D =9² - 4*8 =81 -32 = 49 =7² >0 * * *
(x₁ +x₂)/2=9/2 =4,5 (по теореме Виета);
* * * * * * *
x₁ = 1 ; x₂ = 8. ⇒(x₁ +x₂)/2=(1+8)/2 =4.5.
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7. (0,2)^(x) *(0,2)³ =(0,2)^(2x) / (0,2)⁵ ;
(0,2)^(x+3)=(0,2)^(2x-5) ;
x+3 = 2x-5 ;
x =8.
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8. f(x)= 2,75^(8x+2) ≤ 16/121 ; f(x)= 2,75^(8x+2) ≥ 16/121 ⇒
f(x)= 2,75^(8x+2) = 16/121 .
(11/4) ^(8x+2) = 16/121 ;
(11/4) ^(8x+2) =(11/4) ^(-2) ;
8x+2 = -2 ;
8x = - 4 ;
x = -1/2 .
* * * * * * *
УДАЧИ !!!