Calculators have taken some of the mystery out of this once-challenging question. You can answer the question without a calculator, though.

a. Find an equation for the line through the origin tangent to the graph of y = ln x.

b. Give an argument based on the graphs of y = ln x and the tangent line to explain why ln x

c. Show that ln (x^e)

d. Conclude that x^e

e. So which is bigger, π^e or e^π?

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