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

no real solutions;

one real solution;

two real solutions;

three real solutions.

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

So the possible solutions are \(y=1\), \(y=2\), \(y=-2\). But \(y=2^x>0\) for real \(x\), so valid solutions occur when \(y=1\) or \(y=2\).

This gives the solutions \(x=0\) and \(x=1\) respectively, but since we’re only asked how many solutions there are, we don’t actually need to find them (provided we can be sure they exist!)

So the equation has two real solutions. The answer is (c).