William Stein wrote:

>     * Many engineers, biologists, astronomers, and some others write
> only "ln(x)" or "log_e(x)" when they mean the natural logarithm of x,
> and take "log(x)" to mean log_10(x) or, in computer science, log2(x).

That has been pretty much my experience here in the UK - just in case 
its usage is different in different countries.

Electrical engineers used 'j' for sqrt(-1) too. We use the letter 'i' to 
mean current.

FWIW, Mathematica uses:

In[1]:= ?Log
Log[z] gives the natural logarithm of z
      (logarithm to base e). Log[b, z] gives the logarithm to base b.

But also has Log2 and Log10. (I must admit, until a minute ago, I never 
knew about the latter two. It was only when searching I found these:

In[2]:= ?Log*
Log                   LogicalExpand         LogLogPlot
Log10                 LogIntegral           LogNormalDistribution
Log2                  LogisticDistribution  LogPlot
LogBarnesG            LogitModelFit         LogSeriesDistribution
LogGamma              LogLinearPlot

In[3]:= ?Log2
Log2[x] gives the base-2 logarithm of x.

In[4]:=
In[4]:= ?Log10
Log10[x] gives the base-10 logarithm of x.



>   * In most commonly used computer programming languages, including C,
> C++, Java, Haskell, Fortran, Python, Ruby, and BASIC, the "log"
> function returns the natural logarithm. The base-10 function, if it is
> available, is generally "log10."




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