BMSAT Kozhikode (QA) PYQs

Simplify the following: $\dfrac{1}{\log_{8}(x)} - \dfrac{1}{\log_{7}(x)} + \dfrac{1}{\log_{6}(x)} - \dfrac{1}{\log_{5}(x)} + \dfrac{1}{\log_{4}(x)} - \dfrac{1}{\log_{3}(x)} + \dfrac{1}{\log_{2}(x)}$

If $y > 0,$ and $\log_{y}(x) = 4, \log_{10y} (25x) = 2$ hold, what is $y?$