Logarithms

The idea

$\log_a b = c$ means $a^c = b$. The laws: $\log a + \log b = \log ab$, $\log a - \log b = \log\frac{a}{b}$ and $\log a^n = n\log a$. Take logs of both sides to solve $a^x = b$.

1. Combine logs into a single log using the laws.
2. Turn $\log_a(\dots) = c$ into $(\dots) = a^c$.
3. For $a^x = b$: $x = \frac{\ln b}{\ln a}$. Check every log argument is positive.

Watch out $\log(a + b)$ does not split into $\log a + \log b$.