1961 AHSME Problem 19

Consider the graphs of y=2\log{x} and y=\log{2x}. We may say that:

\begin{array}{l} \textbf{(A)}\ \text{They do not intersect}\qquad \\ \textbf{(B)}\ \text{They intersect at 1 point only}\qquad \\ \textbf{(C)}\ \text{They intersect at 2 points only} \qquad \\ \textbf{(D)}\ \text{They intersect at a finite number of points but greater than 2} \qquad \\ \textbf{(E)}\ \text{They coincide} \end{array}

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