Over a million developers have joined DZone.
{{announcement.body}}
{{announcement.title}}

Another Reason Natural Logarithms Are Natural

DZone's Guide to

Another Reason Natural Logarithms Are Natural

· Big Data Zone
Free Resource

NoSQL & Big Data Integration through standard drivers (ODBC, JDBC, ADO.NET). Free Download

In mathematics, log means natural logarithm by default; the burden of explanation is on anyone taking logarithms to a different base. I elaborate on this a little here.

Looking through Andrew Gelman and Jennifer Hill’s regression book, I noticed a justification for natural logarithms I hadn’t thought about before.

We prefer natural logs (that is, logarithms base e) because, as described above, coefficients on the natural-log scale are directly interpretable as approximate proportional differences: with a coefficient of 0.06, a difference of 1 in x corresponds to an approximate 6% difference in y, and so forth.

This is because

exp(x) ≈ 1 + x

for small values of x based on a Taylor series expansion. So in Gelman and Hill’s example, a difference of 0.06 on a natural log scale corresponds to roughly multiplying by 1.06 on the original scale, i.e. a 6% increase.

The Taylor series expansion for exponents of 10 is not so tidy:

10x ≈ 1 + 2.302585 x

where 2.302585 is the numerical value of the natural log of 10. This means that a change of 0.01 on a log10 scale corresponds to an increase of about 2.3% on the original scale.

Related post: Approximation relating lg, ln, and log10

Easily connect any BI, ETL, or Reporting tool to any NoSQL or Big Data database with CData Drivers (ODBC, JDBC, ADO.NET). Download Now

Topics:

Published at DZone with permission of John Cook, DZone MVB. See the original article here.

Opinions expressed by DZone contributors are their own.

{{ parent.title || parent.header.title}}

{{ parent.tldr }}

{{ parent.urlSource.name }}