Can anyone explain to me step by step how the following proof proceeds, specifically the last part:
For $a$ and $b$, $a > b > 0$, the Euclidean algorithm takes $n$ steps. Then $b > F_n$ so that $b > \phi^{n-1}$, and $n - 1 < \frac{log_{10}b}{log_{10}\phi}$.
How do we reach that last fraction with logarithms?
Proof is on the following page.