The graph of `y=log_(e)x` is as follows.
To draw the graph of `y=|log_(e)x|`, we follow the following procedure.
(i) For `xge1,log_(e)xge0,` so the graph of `y=|log_(e)x|` coincides with that of `y=log_(e)x`.
(ii) For `0ltxlt1,log_(e)xlt0,` so flip the graph of `y=log_(e)x` over the x-axis.
Hence we have the graph of `y=|log_(e)x|` as shown in the following figure.
From the graph, we can see that `y=|log_(e)x|` is non-differentiable at x=1.
