# Why does Wolfram Alpha handle $\log$ and $\ln$ the same?

I thought $\log(n)$ was like $100^x = n$ and $\ln(n)$ was $e^x = n$. But when I do $\ln(80)$, it gives me the answer for $\log$. Why is that?

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Because Alpha tries to be compatible with the syntax of most softwares that may use $\log$ as well as $\ln$. If you want the decimal logarithm try $\log10(x)$. –  Raymond Manzoni Mar 3 '12 at 15:02

It's simply a matter of definitions.

In all fields, $\ln$ means the natural log, or log base $e$, so that $\ln n = x$ whenever $e^x = n$. In engineering (and high school), $\log$ usually means the common log, or log base $10$, so that $\log n = x$ whenever $10^x = n$.

However, it happens that in higher mathematics, the common log just isn't very important. So for convenience, mathematicians often use the notation $\log$ to represent the natural log. Wolfram Alpha does things the same way.

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"engineering (and high school)" - lol –  Salech Alhasov Mar 3 '12 at 20:46
In theoretical mathematics and in many programming languages "$\log$" usually means natural (base-$e$) logarithm. That's the only logarithm that's important for most theoretical purposes.