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If $f(x)$ and $g(x)$ are two functions such that
$$f(x) \in \Theta(g(x))$$$$f(x) \not\in \Omega(g(x))$$
does
$$\log f(x) \in \Theta(\log g(x))$$$$\log f(x) \not\in \Omega(\log g(x))$$
hold?
$$f(x) \in \Theta(g(x))$$
$$\log f(x) \in \Theta(\log g(x))$$
$$f(x) \not\in \Omega(g(x))$$
$$\log f(x) \not\in \Omega(\log g(x))$$
