• $$3^2-2^3=1$$
• $\forall_{a\ b\ >\ 0}\quad a^{\log(b)}\ =\ b^{log(a)}$

Oh, this time the inline code between the dollar signs should work too. But what about accidental appearances of the dollar (I've replaced the actual dollar sign with the word dollar, because the dollar signs mess up the text) sign, like the previous one and this one? Perhaps no space is allowed? (nope, no non-latex dollar signs are allowed or else) Anyway, let me try:

• $3^2-2^3=1$
• $\forall_{a\ b\ >\ 0}\quad a^{\log(b)}\ =\ b^{log(a)}$

Does it work?--Hey, life is good, all three modes of presenting latex work! :-)

The script mentions in-line code too (between single dollar signs). Let's try   $\log(a\cdot b) = \log(a) + log(b)$.   How is it?

It's good! :-)