1958 AHSME Problem 17

If x is positive and \log{x} \ge \log{2} + \frac{1}{2}\log{x}, then:

\begin{array}{l} \textbf{(A)}\ {x}\text{ has no minimum or maximum value}\qquad \\ \textbf{(B)}\ \text{the maximum value of }{x}\text{ is }{1}\qquad \\ \textbf{(C)}\ \text{the minimum value of }{x}\text{ is }{1}\qquad \\ \textbf{(D)}\ \text{the maximum value of }{x}\text{ is }{4}\qquad \\ \textbf{(E)}\ \text{the minimum value of }{x}\text{ is }{4} \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.