# 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

but I'm not entirely sure if this is referring to log base $10$ or the natural logarithm.

In mathematics, $$\log n\log n$$ is most often taken to be the natural logarithm. The notation $$\ln(x)\ln(x)$$ not seen frequently past multivariable calculus, since the logarithm base $$1010$$ finds relatively little use.
This Wikipedia page gives a classification of where each definition, that is base $$22$$, $$ee$$ and $$1010$$, are used:
$$\log (x)\log (x)$$ refers to $$\log_2 (x)\log_2 (x)$$ in computer science and information theory.
$$\log(x)\log(x)$$ refers to $$\log_e(x)\log_e(x)$$ or the natural logrithm in mathematical analysis, physics, chemistry, statistics, economics, and some engineering fields.
$$\log(x)\log(x)$$ refers to $$\log_{10}(x)\log_{10}(x)$$ in various engineering fields, logarithm tables, and handheld calculators.