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| Math Central | Quandaries & Queries |
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Question from Indrajit, a student: (x/10)^(logx - 2)<100..........how to solve this one?? i tried by takng logx = a then taking log on both sides (i took log base 10) then the equation came as (a-2)(a-1)<2.... i don't know whether i did it right or wrong...but plz help me out on this one?... |
Hi Indrajit. I think what you've done is sensible.
Recall that (a-2)(a-1) is a quadratic.
Thus (a-2)(a-1) < 2 becomes a(a-3) < 0. Thus, a > 0 and (a-3) < 0 in
order to have a negative times a positive to make the product < 0.
This means that 0 < a < 3. Now revert to logx = a and exponentiate with
base 10.
1 < x < 1000.
I did a quick graph and it looks correct.
Hope this helps,
Stephen La Rocque.
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