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The function $\dfrac 1{3-\log_5(x)}$ is given. I know the answer, but what I really need to know is how to actually find the domain without outside help.

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    $\begingroup$ At which points does the denominator give you zero values or is undefined (meaning the domain of the base $5$ log function)? You just need to exclude them. $\endgroup$
    – Moo
    Sep 25, 2016 at 1:04
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    $\begingroup$ Also check the domain of a log function. $\endgroup$
    – trang1618
    Sep 25, 2016 at 1:05
  • $\begingroup$ I might as well remove this, I over thought this question. I see now that $log_5(125)$ equals 3, which provides error at this point. $\endgroup$
    – Revinous
    Sep 25, 2016 at 1:09
  • $\begingroup$ Also $x = 0$ as that log is undefined there! $\endgroup$
    – Moo
    Sep 25, 2016 at 1:10

1 Answer 1

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at first it must be $$x>0$$ and the denominator must be $$3-\log_5(x)\neq 0$$ if so we obtain $$\log_5 5^3=\log_5 (x)$$ thus we get $$x=5^3$$ thus we have $$x>0$$ and $$x\ne 5^3$$

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