1954 AHSME Problem 38

If \log 2=.3010 and \log 3=.4771, the value of x when 3^{x+3}=135 is approximately:

\textbf{(A)}\ 5 \qquad \textbf{(B)}\ 1.47 \qquad \textbf{(C)}\ 1.67 \qquad \textbf{(D)}\ 1.78 \qquad \textbf{(E)}\ 1.63

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