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