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Q)

If $log\:_{5.2^{x}+1}^{2}$, $log\:_{2^{x-1}+1}^{4}$ and 1 are in HP, then

$(a)\;x\;is\;an\;integer\qquad(b)\;x\;is\;+ve\;real\qquad(c)\;x\;is\;-ve\;real\qquad(d)\;x\;is\;rational\;but\;not\;integer$

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