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Topic: logarithm (Read 855 times) |
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Christine
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How to prove without using calculus
log x <= sqrt (x) for all natural x?
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pex
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Re: logarithm
« Reply #1 on: Jun 1st, 2012, 11:03am » |
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How do you define log x without using calculus?
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Christine
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Re: logarithm
« Reply #2 on: Jun 1st, 2012, 11:49am » |
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on Jun 1st, 2012, 11:03am, pex wrote:| How do you define log x without using calculus? |
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If log x^2 <= sqrt(x^2) then 2*log x <= x
for x positive integer
As for the problem, I thought perhaps we could use induction. Not sure how. I need some help.
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| « Last Edit: Jun 1st, 2012, 11:51am by Christine » |
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pex
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Re: logarithm
« Reply #3 on: Jun 1st, 2012, 12:11pm » |
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on Jun 1st, 2012, 11:49am, Christine wrote:If log x^2 <= sqrt(x^2) then 2*log x <= x
for x positive integer
As for the problem, I thought perhaps we could use induction. Not sure how. I need some help. |
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Let me rephrase. Which properties of the logarithm can we use? For example, you're using log x2 = 2 log x, but I think we need calculus to prove that property.
So what I meant to ask was, which definition of the logarithm are you using? Which properties we can use, will follow from that.
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