Question

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Answer 1

$1) \ 25^{x}=5^{3-x}\\\\(5^{2})^{x} =5^{3-x}\\\\5^{2x}=5^{3-x}\\\\2x=3-x\\\\2x+x=3\\\\3x=3\\\\\boxed{x=1}$

$2) \ 4^{x}=2^{6+x-x^{2} }\\\\(2^{2}) ^{x}=2^{6+x-x^{2} }\\\\2^{2x}=2^{6+x-x^{2} }\\\\2x=6+x-x^{2} \\\\2x-6-x+x^{2}=0\\\\x^{2}+x-6=0\\\\D=1^{2} -4\cdot(-6)=1+24=25=5^{2}\\\\x_{1} =\dfrac{-1-5}{2} =-3\\\\x_{2}=\dfrac{-1+5}{2}=2\\\\Otvet:\boxed{-3 \ ; \ 2}$

$3) \ 3^{x^{2}-5x+8 }=9 \\\\3^{x^{2}-5x+8 }=3^{2} \\\\x^{2}-5x+8=2\\\\x^{2}-5x+8-2=0\\\\x^{2}-5x+6=0\\\\D=(-5)^{2} -4\cdot6=25-24=1\\\\x_{1}=\dfrac{5-1}{2}=2\\\\x_{2} =\dfrac{5+1}{2} =3\\\\Otvet:\boxed{2 \ ; \ 3}$

Answer 2

Ответ: 1) x=1, 2) -3;2. 3) 2;3