The equation \[8^x+4=4^x+2^{x+2}\] has

  1. no real solutions;

  2. one real solution;

  3. two real solutions;

  4. three real solutions.

[A real solution is one that lies on the number line.]

This equation looks difficult because the unknown \(x\) is in the exponents. Could we make a substitution to make it look more like a familiar type of equation?