Order of operations for solving for x

Question

What is the order of operations for solving any variable? I assumed it was the opposite of PEMDAS, but in $2x^2 = 4$, you have to deal with the exponent first before dividing out to get a correct answer which breaks the order. Unlike $5^{(2x^2-1)} = 25$ which when you make the bases the same is $2x^2-1=2$. From here the answer is $\sqrt{\frac{3}{2}}$ versus $\frac{\sqrt{3}}{2}$. This confuses me. What is the correct order or are there rules etc? Also as a side question, how are logs and roots treated in PEMDAS?