How many real roots does $8^x+4=4^x+2^{x+2}$ have?

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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?