Math CentralQuandaries & Queries


Question from Indrajit, a student:

(x/10)^(logx - 2)< 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?...
how will i get the value of x??

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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