Given $H(x) = lg(f(n))$, where $f(n)$ is an asymptotically positive function, is it always true that if $f(n) = \Theta(g(n))$, then
$H(x) = lg(\Theta(g(n)))$
$\Rightarrow H(x) = \Theta(lg(g(n)))$
To illustrate, Is $lg(n + c) = \Theta(lg(n))$ provided that $c > 0$ and $c$ is a big number?