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Solve log[base 2] x=cx

Source: ISI (BS) 2006 #8

June 2, 2012
logarithmslimitalgebra proposedalgebra

Problem Statement

Show that there exists a positive real number x≠2x\neq 2 such that log⁡2x=x2\log_2x=\frac{x}{2}. Hence obtain the set of real numbers cc such that log⁡2xx=c\frac{\log_2x}{x}=c has only one real solution.
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