Question

Решите уравнения :

$27 \times {3}^{x - 2} - {3}^{ x} = 169$
${7}^{2x} - 49 {}^{7x} = 0$
$3 \times {4}^{x} + {6}^{x} - 2 \times {9}^{x} = 0$
${3}^{x + 1} + {3}^{x - 1} - 10 = 0$
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Answer 1

3^(3+x-2)-3^x=169

3*3^x-3^x=169

2*3^x=169

3^x=169/2

x=log3 169/2

7^(2x)=7^(14x)

2x=14x

x=0

3*(4/9)^x+(6/9)^x-2=0

3*(2/3)^(2x)+(2/3)^x-2=0

(2/3)^x=t

3t^2+t-2=0

D=25

t1,2=(-1+-5)/6=-1, 2/3

(2/3)^x=-1

x=пустое множество

(2/3)^x=2/3

x=1

3*3^x+(1/3)*3^x=10

3^x(3+1/3)=10

3^x=10/10/3=3

x=1