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?

Following up on Jaeyong Chung's answer, and working it out:
$$ 1 =\log_3x\log_4x\log_5x$$
$$1=\frac{(\ln x)^3}{\ln3\ln4\ln5}$$
$$(\ln x)^3 = \ln3\ln4\ln5$$
$$(\ln x) = \sqrt[3]{\ln3\ln4\ln5}$$
$$x = \exp\left(\sqrt[3]{\ln3\ln4\ln5}\right) \approx 3.85093$$
EDIT: And, of course, the obvious answer that everyone will overlook: $x=1$ makes both sides of the equation zero. :D
