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There are two different notation of writing logarithms. In my country (Indonesia), the notation of writing logarithms is

$$ ^a\log b $$

but the most commonly used notation is

$$ \log_{a}b $$

I'm used to the widely used notation. I've searched the web for why there are two different notation, but I couldn't find any. This is only thing I could find relating to that which is what I've explained above that I already know. Are there any historical reasons for this?

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  • $\begingroup$ I'm from Singapore (geographically close and not that different culturally) and I've never seen the former notation. $\endgroup$
    – Deepak
    May 24 '20 at 10:03
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    $\begingroup$ This question belongs on hsm.se. $\endgroup$
    – J.G.
    May 24 '20 at 10:05
  • $\begingroup$ @Deepak That's why I'm asking this. I don't get why we need to use a different notation. Especially if it's not commonly used internationally. $\endgroup$
    – Faris
    May 24 '20 at 10:07
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Based on the comment by @J.G., I researched to the HSM Stack Exchange website. I found this answer there. It is the same book that is also suggested by @bjcolby15. Apparently, it is also widely used in the Netherlands. Considering that Indonesia was colonized by the Dutch, I think the most reasonable explanation is the Indonesians adapted the notation from the Dutch.

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Try this - I found it on the Internet Archive...History of Mathematical Notation, Volume II...the link will bring you right to the section related to logarithms.

I like the Indonesian version $^a\log b$ because it indicates the base a lot more clearly (versus the current convention $\log_a b$), but when they started typesetting mathematical books in the $16$th century, the writers discovered that the base might have been misunderstood as a power (i.e. $b^a$), so to avoid confusion, the current convention of placing the base under the logarithm was used.

Another convention: some mathematicians will use $\log a$ for different bases. For instance, $\log a$ could represent the natural logarithm $\ln a$, the common logarithm $\log_{10} a$, or any base they choose. For the layman, it's confusing unless the base is specifically defined (i.e. "Throughout this book, $\log x$ means the natural logarithm, often denoted $\ln x$; the common logarithm will be represented by $\log_{10} x$.")

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  • $\begingroup$ Thanks for the suggestion. But I think I already found the answer. You can take a look at my answer. $\endgroup$
    – Faris
    May 24 '20 at 10:48
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    $\begingroup$ Agreed. It makes complete sense - and I had forgotten Indonesia was once a Dutch colony, so this was a holdover from that era. $\endgroup$
    – bjcolby15
    May 24 '20 at 11:14
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    $\begingroup$ I don't think that your statement that "In America, $\log a$ represents base $10$" is entirely accurate. This is not a national thing, but rather an indication of what field one works in. As an American mathematician, I use $\log$ to denote the natural logarithm---this seems to be common among mathematicians. Engineers typically use $\log$ to mean the "common logarithm" (i.e. the log base $10$), and some computer scientists use $\log$ to denote the logarithm base $2$ (other use $\lg$ for this). $\endgroup$
    – Xander Henderson
    May 24 '20 at 14:19
  • $\begingroup$ @XanderHenderson: Good catch...I've updated my post. $\endgroup$
    – bjcolby15
    May 24 '20 at 15:52

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