Question

(2^(x-3))^(x+4)=0.5^x*4^(x-4)

Answer 1

Ответ: x₁=-2     x₂=2.

Объяснение:

$\displaystyle\\2^{{(x-3)}^{x+4}}=0,5^x*4^{x-4}\\\\2^{(x-3)*(x+4)}=(\frac{1}{2})^x*\frac{4^x}{4^4}\\ \\2^{x^2-3x+4x-12}={\frac{(\frac{4}{2})^x }{{(2^2)^4} }} \\\\2^{x^2+x-12}=\frac{2^x}{2^8} \\\\2^{x^2+x-12}=2^{x-8}\ \ \ \ \ \ \Rightarrow\\\\x^2+x-12=x-8\\\\x^2-4=0\\\\x^2-2^2=0\\\\(x+2)*(x-2)=0\\\\x_1=-2.\ \ \ \ x_2=2.$