Solve for $x$: question on logarithms. The question:
$$\log_3 x \cdot \log_4 x \cdot \log_5 x = \log_3 x \cdot \log_4 x \cdot \log_5 x \cdot \log_5 x \cdot \log_4 x \cdot \log_3 x$$
My mother who's a math teacher was asked this by one of her students, and she can't quite figure it out. Anyone got any ideas?

The "change-of-base" formula should at least allow you to reduce this to
$$\log_3 x \cdot \left(\frac{\log_4 x}{\log_4 3}\right) \cdot \left(\frac{\log_5 x}{\log_5 3}\right) \ =  \ (\log_3 x)^3 \ = \ \frac{1}{\log_4 3 \cdot \log_5 3} . $$
The number won't be "pretty"...
