1950 AHSME Problem 18

Of the following

(1) a(x-y)=ax-ay

(2) a^{x-y}=a^x-a^y

(3) \log (x-y)=\log x-\log y

(4) \frac{\log x}{\log y}=\log{x}-\log{y}

(5) a(xy)=ax \cdot ay

\begin{array}{l} \textbf{(A)}\ \text{Only 1 and 4 are true}\qquad\\\textbf{(B)}\ \text{Only 1 and 5 are true}\qquad\\\textbf{(C)}\ \text{Only 1 and 3 are true}\qquad\\\textbf{(D)}\ \text{Only 1 and 2 are true}\qquad\\\textbf{(E)}\ \text{Only 1 is true} \end{array}

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