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The touches of y=a^x and y = log{a} x

Explore the following questions with the applet below. 1. When and where would the graphs of y = a^x and y = log {a} x touch each other? Enter the corresponding values of a in terms of e (the base of natural logarithm) in the input box to verify your answer. 2. How many possible points of intersections are there? What is the corresponding condition of a for each of the numbers of intersections?