Answer
$\frac{ln3}{2ln3+ln4}\approx0.307$
Work Step by Step
Step 1. Take logarithm on both sides to get $(1-2x)ln3=xln4 \longrightarrow (2ln3+ln4)x=ln3 \longrightarrow x=\frac{ln3}{2ln3+ln4}\approx0.307$
Step 2. Check $x=\frac{ln3}{2ln3+ln4}\approx0.307$ fits the original equation.