Let \( \log _{2} x+\log _{4} x+\log _{8} x=\log _{k} x \) for all \( x \in R^{+} \). If \( k=\sq...

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Let \( \log _{2} x+\log _{4} x+\log _{8} x=\log _{k} x \) for all \( x \in R^{+} \). If \( k=\sqrt[b]{a} \) where \( a, b \in N \) then find the smallest positive value of \( (a+b) \).
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