If \( \log _{5} 2, \log _{5}\left(2^{x}+1\right) \) and \( \log _{5}\left(2^{x}+5 / 2\right) \) ...

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If \( \log _{5} 2, \log _{5}\left(2^{x}+1\right) \) and \( \log _{5}\left(2^{x}+5 / 2\right) \) are in \( \mathrm{A.P.}\) then \( x \) is equal to
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