Logariddim

Algebra Level 3

(logb2)0(logb520)+(logb2)1(logb521)+(logb2)2(logb522)+(\log_{b} 2)^{0}\left(\log_{b} 5^{2^{0}}\right) + (\log_{b} 2)^{1}\left(\log_{b} 5^{2^{1}}\right) + (\log_{b} 2)^{2}\left(\log_{b} 5^{2^{2}}\right) + \cdots

If b=100,b = 100, what is the infinite sum above?

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