Answer
$\frac{26\pm8\sqrt {10}}{9}\approx0.078, 5.700$
Work Step by Step
Step 1. Rewrite the equation $\frac{ln(3x+2)}{ln2}-\frac{ln(x)}{ln2^2}=3 \longrightarrow 2ln(3x+2)=6ln2+ln(x) \longrightarrow (3x+2)^2=64x \longrightarrow 9x^2-52x+4=0 \longrightarrow x=\frac{52\pm\sqrt {52^2-4(4)(9)}}{2(9)}=\frac{26\pm8\sqrt {10}}{9}\approx0.078, 5.700$
Step 2. Check, $x=\frac{26\pm8\sqrt {10}}{9}\approx0.078, 5.700$ fit the original equation.
