Answer
$\{-5.057 \}$
Work Step by Step
Step 1. Take natural logarithm on both sides to get $(x-4)ln3=(2x+5)ln7$
Step 2. Solve the above equation: $(ln3-2ln7)x=5ln7+4ln3$, thus $x=\frac{5ln7+4ln3}{ln3-2ln7}\approx-5.057$
Step 3. In set form $\{-5.057 \}$