Logarithms and exponentials¶
In logarithms we ask to what power we must raise the base to get y. If we have a base 10 logarithm:
\[\begin{split}
y = 10^{\log y} \\
\log y = x \\
y = 10^x
\end{split}\]
Natural logarithm¶
Here the base is \(e\)
\[\begin{split}
y = e^{\ln y} \\
\ln y = x \\
y = e^x
\end{split}\]
Rules¶
\[\begin{split}
\log (ab) = \log a + \log b \\
\log (a/b) = \log a - \log b \\
\log(a^n) = n \log(a) \\
\log(1/a) = \log(1) - \log(a) = 0 - \log(a)
\end{split}\]