The graphs of y=1.1x and y=x have two points of intersection, while the graphs of y=2^x and y=x have no points of intersection.  It follows that there is a real number 1 < p<2 for which the graphs of y=p^x and y=x have exactly one point of intersection and y=x is tangent to y=p^x. Find the value of p  Determine the coordinates of the single point of intersection y=p^x and y=x.  Type the values for the x- and y-coordinates or an approximation.

Question

The graphs of y=1.1x and y=x have two points of intersection, while the graphs of y=2^x and y=x have no points of intersection.  It follows that there is a real number 1 < p<2 for which the graphs of y=p^x and y=x have exactly one point of intersection and y=x is tangent to y=p^x.

Find the value of p 

Determine the coordinates of the single point of intersection y=p^x and y=x.  Type the values for the x- and y-coordinates or an approximation.

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