Answer
$log_3(-2+\sqrt 7)\approx-0.398$
Work Step by Step
1. $9^x+4\cdot 3^x-3=0 \Longrightarrow (3^x)^2+4\cdot 3^x-3=0 \Longrightarrow 3^x=\frac{-4\pm\sqrt {16-4(-3)}}{2}=-2\pm\sqrt 7 \Longrightarrow x=log_3(-2+\sqrt 7)\approx-0.398$
2. Check, $x=log_3(-2+\sqrt 7)$ fit(s).
