"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

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- Jan 14th 2009, 06:03 PMUncle6Log comparision question
"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 - Jan 14th 2009, 06:21 PMJhevon
think of it this way:

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 - Jan 15th 2009, 03:50 PMUncle6
Thanks, but it still is quite difficult to understand.

- Jan 15th 2009, 04:49 PMJhevon
- Jan 15th 2009, 07:26 PMUncle6Quote:

in other words, b has the task of increasing the base 5 a larger magnitude (relatively speaking) than a has to do for 3