Answer
$\frac{26\pm 8\sqrt {10}}{9}\approx0.078,5.700$
Work Step by Step
1. $log_2(3x+2)-log_4(x)=3 \Longrightarrow \frac{log(3x+2)}{log2}-\frac{log(x)}{log4}=3 \Longrightarrow \frac{log(3x+2)}{log2}-\frac{log(x)}{2log2}=3\Longrightarrow 2log(3x+2)-log(x)=6log2 \Longrightarrow (3x+2)^2=64x \Longrightarrow 9x^2-52x+4=0 \Longrightarrow x=\frac{52\pm\sqrt {52^2-4(9)(4)}}{2(9)}=\frac{26\pm 8\sqrt {10}}{9}\approx0.078,5.700$
2. Check, $x=\frac{26\pm 8\sqrt {10}}{9}$ fit.
