Question

Решите, пожалуйста, показательные уравнения №268

Answer 1

$x^{2} *3^{x}-3^{x+1}=0\\\\x^{2}*3^{x}-3^{x}*3=0\\\\3^{x}(x^{2}-3)=0\\\\3^{x} \neq 0\\\\x^{2}-3=0\\\\x_{1}=\sqrt{3}\\\\x_{2}=-\sqrt{3}$

$2)x^{2}*5^{x}-5^{2+x}=0\\\\x^{2}*5^{x}-5^{2} *5^{x} =0\\\\5^{x}(x^{2}-25)=0\\\\5^{x}\neq 0\\\\x^{2}-25=0\\\\x_{1}=5\\\\x_{2}=-5$

$3)x^{3}*3^{x}+3^{x+3}=0\\\\x^{3}*3^{x}+3^{x}*3^{3}=0\\\\3^{x}(x^{3}+3^{3})=0\\\\3^{x} \neq 0\\\\x^{3}+27=0\\\\x^{3}=-27\\\\x=\sqrt[3]{-27}\\\\x=-3$

$4)x^{3}*8^{x}-8^{x+1}=0\\\\x^{3}*8^{x}-8^{x}*8=0\\\\8^{x}(x^{3}-8)=0\\\\8^{x}\neq 0\\\\x^{3}-8=0\\\\x^{3}=8\\\\x=\sqrt[3]{8}\\\\x=2$