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I need to state a value of \(x\) so that \({log_3 x}\) is:

 

a) a positive integer

b) a negative integer

c) a rational number

 

How should I do this? I tried using its exponential form (\({3^x}\)) but it's not helpful...

My guess for c) is that x > 0 since rational numbers include all positive and negative numbers, zero, and fractions, and x must be greater than 0 because of the asymptote.

 Apr 23, 2019
edited by Guest  Apr 23, 2019
edited by Guest  Apr 23, 2019
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\(a)~\text{any positive integer power of 3:}~3, 9, 27, 81, \text{ etc.}\\ b)~\text{any negative integer power of 3:}~\dfrac 1 3,\dfrac 1 9,\dfrac{1}{27},\dfrac{1}{81}\\ c)~\text{any rational power of 3:}\sqrt{3},3\sqrt{3},\sqrt[3]{3}\text{ etc.}\)

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 Apr 23, 2019

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