1950 AHSME Problem 37

If y =\log_{a}{x}, a>1, which of the following statements is incorrect?

\begin{array}{l} \textbf{(A)}\ \text{If }x=1,y=0\qquad\\ \textbf{(B)}\ \text{If }x=a,y=1\qquad\\ \textbf{(C)}\ \text{If }x=-1,y\text{ is imaginary (complex)}\qquad\\ \textbf{(D)}\ \text{If }0<x<1,y\text{ is always less than 0 and decreases without limit as }x\text{ approaches zero}\qquad\\ \textbf{(E)}\ \text{Only some of the above statements are correct} \end{array}

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