The definition of the number e is another area where the previous development was somewhat incomplete. For example, we did not study how to treat exponential functions with exponents that are irrational. However, we glossed over some key details in the previous discussions. We already examined exponential functions and logarithms in earlier chapters. 6.7.7 Express general logarithmic and exponential functions in terms of natural logarithms and exponentials.6.7.6 Prove properties of logarithms and exponential functions using integrals.6.7.5 Recognize the derivative and integral of the exponential function.6.7.4 Define the number e e through an integral.6.7.3 Integrate functions involving the natural logarithmic function.6.7.2 Recognize the derivative of the natural logarithm.6.7.1 Write the definition of the natural logarithm as an integral.
