# Schröder equation

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For a given function $f$ and constant $c$ find a function $\sigma$ such that $$\sigma(f(x))=c \sigma(x).$$

The Schröder equation can be transformed into the form of an Abel equation: $$\log_c\!\Big(\sigma\big(f(x)\big)\Big)=1+\log_c(\sigma(x))$$