Graphing logarithmic functions from exponential functions

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! textbook explanation on deriving the graph of a logarithmic function[]1

In this write up the author interchanged the axes and then reflected the graph. But this is supposed to be the same thing, the author interchanged the axes, but the graph didn't change in fig.3.3. I know for a fact that the graph of a logarithmic function the same as reflecting the graph of an exponential function about the line y=x. Is this explanation wrong?