ln() vs. log()

[Thomas Klemm]

(04-17-2016 10:19 PM)Han Wrote:  That is \( \ln(x) = \frac{\log(x)}{\log(10)} \) with log just being a conventional shortcut for \( \log_{10}\).

But then \(\log_{10}(10) = 1\) and thus:

\(
\begin{align}
\ln(x)
&= \frac{\log(x)}{\log(10)} \\
&= \frac{\log_{10}(x)}{\log_{10}(10)} \\
&= \frac{\log_{10}(x)}{1} \\
&= \log_{10}(x) \\
&= \log(x) \\
\end{align}
\)

Thus, you either meant:

\(
\ln(x) = \frac{\log(x)}{\log(e)}
\)

Or then:

\(
\log(x) = \frac{\ln(x)}{\ln(10)}
\)