Logarithm square root problem

Need some help with a log equation. I've done some searching and I found a very similar problem but didn't understand the response / solution.

$\displaystyle \sqrt{\log{x}}=\log{\sqrt{x}}$

This was the partial solution:

http://www.mathhelpforum.com/math-he...4b006d6c-1.gif

http://www.mathhelpforum.com/math-he...5be1e333-1.gif

http://www.mathhelpforum.com/math-he...4ff8d308-1.gif

set each factor equal to 0 and solve for x

I get the first two lines, but I don't see how we go from http://www.mathhelpforum.com/math-he...5be1e333-1.gif to http://www.mathhelpforum.com/math-he...4ff8d308-1.gif

and I definitely don't get where to go from there. (Headbang)

Note, my equation uses base 10 logs, where the solution I found uses natural logs. That shouldn't matter, though, as I'm more interested in the mechanics of *how* to solve it than the actual solution.

Any help is greatly appreciated...

Thanks in advance!