Positive real numbers a and b have the property that
\sqrt{\log a}+\sqrt{\log b}+\log \sqrt{a}+\log \sqrt{b}=100
and all four terms on the left are positive integers, where log denotes the base 10 logarithm. What is a b ?
Answer Choices
A. 10^{52}
B. 10^{100}
C. 10^{144}
D. 10^{164}
E. 10^{200}