When log is written without a base, is the equation normally referring to log base 10 or natural log? For example, this question presents the equation
$$\omega(n) < \frac{\log n}{\log \log n} + 1.4573 \frac{\log n}{(\log \log n)^{2}},$$
but I'm not entirely sure if this is referring to log base $10$ or the natural logarithm. 
 A: In mathematics, $\log n$ is most often taken to be the natural logarithm.  The notation $\ln(x)$ not seen frequently past multivariable calculus, since the logarithm base $10$ finds relatively little use.
This Wikipedia page gives a classification of where each definition, that is base $2$, $e$ and $10$, are used:

$\log (x)$ refers to $\log_2 (x)$ in computer science and  information theory.
$\log(x)$ refers to $\log_e(x)$ or the natural logrithm in mathematical analysis, physics, chemistry, statistics, economics, and some engineering fields.
$\log(x)$ refers to $\log_{10}(x)$ in various engineering fields, logarithm tables, and handheld calculators.

A: Depending on the subject, it can be base $10$, base $e$, or base $2$.  Base $2$ is common in computer science.  Base $10$ is popular in engineering (think decibels).  I would take this to be base $e$
A: In some cases, "$\log$" can refer to a logarithm with an indefinite base.
Suppose we're taking the logarithm (base $b$, where $b>0$ is constant) of some variable.
Recall the identity
$$\log_b(x) = \frac{\log_c(x)}{\log_c(b)}$$
The base-$b$ logarithm can be expressed as a constant factor times the logarithm to any other base $c>0$. In some domains, particularly asymptotic analysis, we don't care about constant factors—which means that it doesn't matter what base we pick. So we can unambiguously write $Θ(\log(n))$ without specifying the base.
(This does not apply to the specific usage in the question, which is about an upper bound for all $n$. Obviously constant factors matter there.)
A: If you come from a computer science background, then:

*

*log(x) = log$_{10}$(x)

*ln(x) = log$_{e}$(x)

*lg(x) = log$_{2}$(x)

If a computer scientist is using log(x) with a base that is not 10, then he/she will usually point it out clearly.
A: Generally it is bad practice to write logarithms without the base especially if the context hasn't been sufficiently set up. If a base is to be implied, then it is better to use one of the variants, such as $ln()$ for base $e$, $lg()$ for base $2$, etc.
But there is literature out there that violates the above rule, so yes, you'll need to infer the base from the context.
Having said that, there are cases when a missing base is intentional and acceptable, implying that it is applicable regardless of what the base is. For instance, when I say:
$$log_{2}(10) = log(10)/log(2)$$
and you notice that the base is omitted in the RHS, it means that it is applicable to any base in the RHS (of course, as long as the same base is used in both numerator and denominator).
To me, that is the only acceptable case when one can omit the base.
A: In many programming languages, log is the natural logarithm. There are often variants for log2 and log10.
Checked in C, C++, Java, JavaScript, R, Python
