If \( \log _{2}\left(5.2^{x}+1\right), \log _{4}\left(2^{1-x}+1\right) \) and 1 are in A.P then ...

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If \( \log _{2}\left(5.2^{x}+1\right), \log _{4}\left(2^{1-x}+1\right) \) and 1 are in A.P then \( x \) equals
(A) \( \log _{2} 5 \)
(B) \( 1-\log _{2} 5 \)
(C) \( \log _{5} 2 \)
(D) none of these
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