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I was solving $$\int^\infty_0 \frac{dx}{e^x+1}$$ and the answer was $\log(2)$. However, I used natural logarithm when solving this integral and so I got $\ln(2)$. Would both answers be accepted?

Sebastiano
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ianc1339
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    In mathematics, the general convention for log is to take the natural logarithm. In physics, it is the base-10 log, and in computer science, the base-2 log. So you've got it right :) – Anthony Jan 29 '21 at 22:16
  • @AnthonySaint-Criq do you mean high school physics? I would be genuinely astonished that practicing physicists use base 10 logs in real physics formulas. – KCd Jan 29 '21 at 22:19
  • @KCd I guess it depends, but at least in chemistry that's for sure they use log10. For the physics I did, I don't remember using much logarithms at all in fact, it's more the exponential because differential equations. – Anthony Jan 29 '21 at 22:34
  • It is related to the question I asked few month ago: https://math.stackexchange.com/questions/3918931/why-we-are-allowed-to-use-notation-logx-instead-of-lnxto-denote-logari – Etemon Jan 30 '21 at 14:59

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In mathematics we use denote the natural logarithm by $\log(x)$, You can sometime in old books denote $\ln(x)$ like a natural logarithm, but actually in the new science papers we use $\log(x)$ to denote the natural logarithm.

Joe
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Mathematical notations are mostly a matter of conventions, and understanding notations depends on context.

In mathematics literature, $\log(x)$ has been used for both $\log_{10}(x)$ or $\log_e(x)$.

In complex analysis, you will see that sometimes people use $\log$ as the complex logarithm with base $e$ and reserve $\ln$ as the real logarithm with base $e$.

If you are taking an exam, and you should follow the instructor's definitions. Your solution simply means $\log(2):=\log_e2$.

  • When I was a boy :-) I used also $\operatorname{Log}(x)=\log_{10}(x)$. – Sebastiano Jan 29 '21 at 22:39
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    @Sebastiano: interesting. I have only seen $\textrm{Log}$ used as the principal complex logarithm. –  Jan 29 '21 at 22:41
  • See this Italian link https://www.treccani.it/enciclopedia/logaritmo_%28Enciclopedia-della-Matematica%29/#:~:text=Nella%20tradizione%20italiana%2C%20per%20il,nome%20del%20matematico%20inglese%20H. The traslator say: In the Italian tradition, for the decimal logarithm is sometimes used the notation Log (with capital L). This logarithm in base 10 is also sometimes called vulgar logarithm or Briggs' logarithm, from the name of the English mathematician H. Briggs. – Sebastiano Jan 29 '21 at 22:44