$$ \log_a f $$

$$ (a-1)(f-1) $$

$$ \log_a f - \log_a g $$

$$ (a-1)(f-g) $$

$$ \log_f h - \log_g h $$

$$ (f-1)(g-1)(h-1)(g-f) $$

$$ h^f-h^g $$

$$ (h-1)(f-g) $$

$$ f^h-g^h $$

$$ h(f-g) $$

$$ |f|-|g| $$

$$ (f-g)(f+g) $$