AMC 12A 2013 Problem 14

The sequence

\log _{12} 162, \log _{12} x, \log _{12} y, \log _{12} z, \log _{12} 1250

is an arithmetic progression. What is x ?

Answer Choices
A. 125 \sqrt{3}
B. 270
C. 162 \sqrt{5}
D. 434
E. 225 \sqrt{6}