Correct option is (C) -1
\(log_2\,(log_{25}\,5)\) \(=log_2\,(\frac1{log_{5}\,25})\) \((\because log_b\,a=\frac1{log_a\,b})\)
\(=log_2\,(\frac1{log_{5}\,5^2})\)
\(=log_2\,(\frac1{2\,log_{5}\,5})\) \((\because log\,a^n=n\,log\,a)\)
\(=log_2\,(\frac1{2})\) \((\because log_a\,a=1)\)
\(=log_2\,(2^{-1})\)
\(=-1\,log_2\,2\) = -1
