I promise this isn’t homework, I’m 30 years old.
A friend of mine just took a test where she encountered this problem, as she recalls it:
20[sup]5[/sup] = 2[sup]m[/sup] + 2[sup]n[/sup], solve for mn
without using logs. Although even with logs, I’m not sure how you would do it, because of the +. And then even if she misremembered a + where it was actually a *, I’m still not sure, because I can’t seem to match up the bases, which is how you normally do this (typically simple) type of question.