Hello daparsons Originally Posted by

**daparsons** ... I still don't understand how to solve for x using that process.

The principle is this:

- If the product of two (or more) expressions is equal to zero, then one (or more) of these expressions is itself equal to zero.

The most common example of this is the quadratic equation, where we factorise the quadratic expression (if possible), and then put each factor in turn equal to zero. For example:$\displaystyle x^2-5x+6=0$

$\displaystyle \Rightarrow (x-2)(x-3)=0$

and it's when we put each of these factors in turn equal to zero:$\displaystyle (x-2)=0$

or$\displaystyle (x-3)=0$

that we get the solutions:$\displaystyle x=2$

or$\displaystyle x=3$

Well, we just apply the same principle here. When you get to:$\displaystyle 0 = \sqrt{\log x}(\tfrac12\sqrt{\log x} -1)$

you can then conclude that:$\displaystyle \sqrt{\log x} = 0$

or

$\displaystyle (\tfrac12\sqrt{\log x} -1) = 0$

As has already been pointed out, the first of these possibilities, $\displaystyle \sqrt{\log x} = 0$, doesn't yield any values of $\displaystyle x$. So we're left with the conclusion that the only solution is when $\displaystyle \tfrac12\sqrt{\log x}-1 = 0$; i.e. $\displaystyle x = 10,000$.

Grandad