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Question Number 130119 by Study last updated on 22/Jan/21

lim_(x→15) log(x−15)=?? or limit has?

$${li}\underset{{x}\rightarrow\mathrm{15}} {{m}log}\left({x}−\mathrm{15}\right)=??\:{or}\:{limit}\:{has}? \\ $$

Answered by Olaf last updated on 22/Jan/21

lim_(x→15^− )  ln(x−15) is undefined  because x−15 canno′t be negative  lim_(x→15^+ )  ln(x−15) = lim_(X→0^+ )  lnX = −∞

$$\underset{{x}\rightarrow\mathrm{15}^{−} } {\mathrm{lim}}\:\mathrm{ln}\left({x}−\mathrm{15}\right)\:\mathrm{is}\:\mathrm{undefined} \\ $$$$\mathrm{because}\:{x}−\mathrm{15}\:\mathrm{canno}'\mathrm{t}\:\mathrm{be}\:\mathrm{negative} \\ $$$$\underset{{x}\rightarrow\mathrm{15}^{+} } {\mathrm{lim}}\:\mathrm{ln}\left({x}−\mathrm{15}\right)\:=\:\underset{\mathrm{X}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\mathrm{lnX}\:=\:−\infty \\ $$

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