Question

1) 2^(3x+7)+5^(3x+4)+2^(3x+5)-5^(3x+5)=0 2)2^(-2x+5)-2^(-2x)-3^(-2x+3)-2^(-2x+2)=0

Answer 1

1)
$2^{3x+7}+5^{3x+4}+2^{3x+5}-5^{3x+5}=0 \\2^{3x+5}(2^2+1)+5^{3x+4}(1-5)=0 \\5*2^{3x+5}-4*5^{3x+4}=0 \\5*2^{3x+5}=4*5^{3x+4} \\ 2^{3x+5-2}=5^{3x+4-1} \\2^{3x+3}=5^{3x+3} \\( \frac{2}{5})^{3x+3}=1 \\3x+3=0 \\3x=-3 \\x=-1$
ответ: x=-1
2)
$2^{-2x+5}-2^{-2x}-3^{-2x+3}-2^{-2x+2}=0 \\-2x=y \\2^{y+5}-2^y-3^{y+3}-2^{y+2}=0 \\2^y(2^5-1-2^2)-3^{y+3}=0 \\2^y*27=3^{y+3} \\2^y*3^3=3^{y+3} \\2^y=3^{y+3-3} \\2^y=3^y \\ (\frac{2}{3})^y=1 \\y=0 \\-2x=0 \\x=0$
ответ: x=0