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The inverse of an exponential function is a logarithmic function. The inverse of a function is obtained by switching the x and y coordinates. This reflects the graph about the line y=x. As you can tell from the graph to the right, the logarithmic curve is a reflection of the exponential curve.

from Mrs. E Teaches Math

How I Teach Intro to Logs

How I Teach Properties of Logarithms - ideas for introducing exponential and log functions in Algebra 2