How i can find the domain of a nonnatural logarithmic function? I cant found any information about it. For example, the domain of $f(x) = \log_{3}(x+2)$
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You have to impose $x+2>0$ and for a generic base $g(x)$ that is greater than $0$ and different of $1$ (and this is the case of 3) – pawel Mar 11 '21 at 19:57
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So it is the same procedure for natural logarithmic functions? – Nicolás Castellanos Mar 11 '21 at 20:00
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Any two logarithms are proportional. – Ethan Bolker Mar 11 '21 at 20:01
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Yes but in general if the base is not $e$ you have in addition to check if the base is greater than $0$ and different from 1. Can be useful for you looking at https://en.wikipedia.org/wiki/Logarithm (Look at the 2nd paragraph) – pawel Mar 11 '21 at 20:02
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So, the domain of the example is (-2, infinite) – Nicolás Castellanos Mar 11 '21 at 20:09
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@NicolásCastellanos yes! All works: look at https://www.wolframalpha.com/input/?i=log_3%28x%2B2%29 – pawel Mar 11 '21 at 20:10
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@NicolásCastellanos Anyway if you want to look only at logarithm in natural base you can use the change of base rule – pawel Mar 11 '21 at 20:21
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https://pastebin.com/P65Wj7Qf – Nicolás Castellanos Mar 11 '21 at 21:04
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Please view the link – Nicolás Castellanos Mar 11 '21 at 21:18
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@Nicolás Castellanos Sorry honestly I can't understand what you want to mean with this link... Can you explain it specifically? – pawel Mar 11 '21 at 21:21
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@pawel Do you openned the link? – Nicolás Castellanos Mar 11 '21 at 21:23
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@pawel If you dont understand the text, resume: How to solve log((6x+2)/5) – Nicolás Castellanos Mar 11 '21 at 21:24
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You have simply to impose $\frac{6x+2}{5}>0$ (the base in this case is $e$ surely $>0$ and $\neq 1$). So $\frac{6x+2}{5}>0\iff 6x+2\iff x>\frac{-1}{3} $. Is it what you are interested in? – pawel Mar 11 '21 at 21:27
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@pawel Yes, very thanks – Nicolás Castellanos Mar 11 '21 at 21:28