Chapter 7 - Exponential Functions - 7.1 Derivative of f(x)=bx and the Number e - Exercises - Page 327: 7

$$ x=-\frac{1}{3}.$$

We have $$ 4^{-x}=2^{x+1} \Longrightarrow (2^2)^{-2x}=2^{x+1} \Longrightarrow 2^{-2x}=2^{x+1}. $$ Since the bases are equal, then the exponents are equal and hence we get $$-2x=x+1\Longrightarrow -3x=1\Longrightarrow x=-\frac{1}{3}.$$