AMC 12B 2010 Problem 12

For what value of x does

\log _{\sqrt{2}} \sqrt{x}+\log _{2} x+\log _{4}\left(x^{2}\right)+\log _{8}\left(x^{3}\right)+\log _{16}\left(x^{4}\right)=40 ?

Answer Choices
A. 8
B. 16
C. 32
D. 256
E. 1024