"Which is greater, ? Explain"
Although u can plug and chug into your calculator, this question seems like it's meant to be solved analytically.
I got to:
Dunno what's next. I can figure out that a<2 and ab>2
we have and
Note that 5 is less than twice 3, while 11 is more than twice 5. in other words, has the task of increasing the base 5 a larger magnitude (relatively speaking) than has to do for 3. is larger
this is a more intuitive approach. which i suppose is the level of thinking this problem requires, since it is elementary/middle school math. there are more rigorous proofs, i'm sure