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September 23rd, 2010, 11:21 PM   #1
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Exponential inequality

I hope I'm getting my terms right (I'm Norwegian so we naturally don't use the English math terms).

There's this nasty inequality that I'm struggling to solve. Looks like this:

5^3x < 3 * 5^x

My first instinct was to do this

5^3x - 3 * 5^x = 0

and try to solve it but how?
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September 23rd, 2010, 11:46 PM   #2
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Re: Exponential inequality

My first move would be to divide through by 5^x, since 5^x > 0 for all real x. This gives:

5^(2x) < 3

Next, take the log base 5 of both sides, giving:

2x < log5(3)

x < log5[?(3)]
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