Question

How do you graph `g(x)= log_6 x`?

Answer 1

Using that `log_6(x)` is defined to be the value such that `6^(log_6(x)) = x`, we can find points to plot by using that

`g(6^k)=log_6(6^k) = k` for any choice of `k`. For example, we would have points such as `(1,0), (6, 1), (36, 2)` as well as `(1/6, -1), (1/36, -2)`.

In general, logarithmic functions tend to `-oo` as `x` approaches `0`, so we have a vertical asymptote at `x=0`. After that, you can use some easily plotted points such as the ones above to see approximately how the curve grows. In this case, the graph will be as follows:

graph{log(x)/log(6) [-2, 9, -3.5, 2]}