CAT 2018 Logarithms — Previous Year Question

$\frac{1}{\log_2 100}$ - $\frac{1}{\log_4 100}$ + $\frac{1}{\log_5 100}$ - $\frac{1}{\log_{10} 100}$ + $\frac{1}{\log_{20} 100}$ - $\frac{1}{\log_{25} 100}$ + $\frac{1}{\log_{50} 100}$ = ?