Consider the table below for the function $f\left(x\right) = \operatorname{log}_{b }x$.

1. Complete the table.

   Hint (a):

   Use the logarithm rules to calculate the missing values.

   Example (a):

   $\operatorname{log}_{b} 4 = \operatorname{log}_{b} \left(2^{2}\right) = 2\\\left(\operatorname{log}_{b} 2\right)\operatorname{log}_{b} 4 = 0.5404$

2. Extend the table to include six more x-values of your choice. Show how you calculated the f(x) values for each.

   Hint (b):

   See part (a).

3. Find the base of this logarithmic function and explain how you found it

   Hint (c):

   When does $\operatorname{log}_{b} x = 1?$ If you cannot find this,
   when does $\operatorname{log}_{b} x$ become greater than one?