Conditions for Floor of Log base b of x to equal Floor of Log base b of Floor of x

Theorem
Let $b \in \R$ be a real number.


 * $\forall x \in \R_{\ge 1}: \floor {\log_b x} = \floor {\log_b \floor x} \iff b \in \Z_{> 1}$

where $\floor x$ denotes the floor of $x$.