Question

$log_{0,2x}x + log_{0,1x}x = 0$

Answer 1

$\frac{1}{ log_{x}(0.2x) } + \frac{1}{ log_{x}(0.1x) } = 0 \\ \frac{ log_{x}(0.1x) + log_{x}(0.2x) }{ log_{x}(0.1x) \times log_{x}(0.2x) } = 0 \\ log_{x}(0.1x \times 0.2x) = 0 \\ 0.02 {x}^{2} = 1 \\ x = \sqrt{50}$