For what value of \(x\) is \(\sqrt{2}+\sqrt{2}+\sqrt{2}+\sqrt{2}=2^x\) true?

A)\(\quad \frac{1}{2}\qquad\) B)\(\quad 1\frac{1}{2}\qquad\) C)\(\quad 2\frac{1}{2}\qquad\) D)\(\quad 3\frac{1}{2}\qquad\) E)\(\quad4\frac{1}{2}\)

We have that \(\sqrt{2}+\sqrt{2}+\sqrt{2}+\sqrt{2}=4\sqrt{2}=2^2\times2^{1/2}=2^{2.5}.\)

Thus \(x = 2\frac{1}{2}\), and the answer is (C).