Secant Method - Calculating the number of steps required

I need to calculate the number of steps required to reach a specified accuracy by using the Secant method. Here is the question:

$\displaystyle Secant: |x_{n+1} - r| \leq C_{sct}. |x_n - r|^{\alpha_{sct}} $ with $\displaystyle \alpha_{sct} \approx 1.618$

If an initial guess, $\displaystyle x_0$, is supplied such that $\displaystyle |x_n - r| = 10^{-2}$, and we assume that $\displaystyle C_{sct} = 3$, how many steps of each method are necessary to ensure that $\displaystyle |x_n - r| \leq 10^{-14}$?

Hope someone can help!

Thanks