Chapter 7 - Exponential Functions - 7.1 Derivative of f(x)=bx and the Number e - Exercises - Page 327: 5

$$ x=-\frac{1}{2}.$$

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