0. Mathematical Tricks

Manipulation of Log-Expressions

Switching basis

$a^{lo{g}_b(n)}=n^{lo{g}_b(a)}$

Getting two exponentials together

We often encounter fractions of the form $\frac{a^{kn}}{b^{k^{\prime }n}}=\frac{e^{\ln (a^{kn})}}{e^{\ln (b^{k^{\prime }n})}}=e^{kn\cdot \ln (a)-k^{\prime }n\cdot ln(b)}$