5.3.2 	Exponential and logarithmic functions

The integral of f(x)exp(ax) dx, H. L. Kung, 1:2, 1970, 106, C, 5.2.5
Integration by Undetermined Coefficients, Louise Grinstein, 2:2, 1971, 98-100, 5.2.5
Which is Larger, e^pi or pi^e?, Ivan Niven, 3:2, 1972, 13-15
An Alternate Classroom Proof of the Familiar Limit for e, Norman Schaumberger, 3:2, 1972, 72-73, C
Random Sieving and the Prime Number Theorem, Karl Greger, 5:1, 1974, 41-46, 9.3
Some Comments on the Exceptional Case in a Basic Integral Formula, Norman Schaumberger, 5:3, 1974, 58, C, 5.2.1
Two More Proofs of a Familiar Inequality, Erwin Just and Norman Schaumberger, 6:2, 1975, 45, C
A Geometric Approach to a Basic Limit, Norman Schaumberger, 7:1, 1976, 11-12
Using Inverse Functions in Integration, Robert C. Crawford, 8:2, 1977, 107-109, C, 5.3.3
A Neglected Approach to the Logarithm, Bruce S. Babcock and John W. Dawson, Jr., 9:3, 1978, 136-140, 5.1.1
On the General Power Function, P. S. Chee and S. T. Chin, 11:1, 1980, 51, C
Is Ln the Other Shoe?, Byron L. McAllister and J. Eldon Whitesitt, 12:1, 1981, 20-23, 5.2.1
Obtaining a Numerical Estimate for e, David H. Anderson, 12:1, 1981, 30-33
A "Proof" that 0=1, Norman Schaumberger, 12:3, 1981, 211, C
Euclid's 'Elements' -excerpts from a 1660 edition, 12:2, 1981, 117, 0.3, 5.3.3
Integration by Geometric Insight—A Student's Approach, Ann D. Holley, 12:4, 1981, 268-270, C, 5.2.6, 5.3.1
Motivating e by Calculator, Arthur C. Segal, 13:4, 1982, 271, C
A Nonlogarithmic Proof That (1 +1/n )^n has limit e, Lee Badger, 13:5, 1982, 331-332, C
A Logarithm Algorithm for Four-Function Calculators, David Cusick, 14:4, 1983, 322, 0.2
A Logarithm Algorithm for a Five-Function Calculator, Donald L. Muench and Gerald Wildenberg, 14:4, 1983, 324-326
Another Way to Introduce Natural Logarithms and e, Robert R. Christian, 14:5, 1983, 424-426
Evaluating e^x Using Limits, Sheldon P. Gordon, 15:1, 1984, 63-65, 5.4.2
Inverse Functions, Ralph P. Boas, 16:1, 1985, 42-47, 5.2.1, 5.4.2
Euler's Constant, Frank Burk, 16:4, 1985, 279, C
An Instant Proof of e^pi > pi^e, Norman Schaumberger, 16:4, 1985, 280, C
Using Riemann Sums in Evaluating a Familiar Limit, Frank Burk, 17:2, 1986, 170-171, C, 5.1.1, 5.2.1
The Change of Base Formula for Logarithms, Chris Freiling, 17:5, 1986, 413, C, 0.2
Comparing B^A and A^B for A>B, John Rosendahl and James Gilmore, 18:1, 1987, 50, C
Behold! The Graphs of f and f inverse are Reflections about the Line y=x, Ayoub B. Ayoub, 18:1, 1987, 52, C, 0.2
A Depreciation Model for Calculus Classes, John C. Hegarty, 18:3, 1987, 219-221, C
The Relationship Between Hyperbolic and Exponential Functions, Roger B. Nelsen, 19:1, 1988, 54-56, C, 5.3.3
An Efficient Logarithm Algorithm for Calculators, James C. Kirby, 19:3, 1988, 257-260, C, 9.6
The Age of the Solar System, Winston Phrobis, 21:5, 1990, 399-400, C
The Snowplow Problem Revisited, Xiao-peng Xu, 22:2, 1991, 139, C, 6.1
FFF #44. A New Way to Obtain the Logarithm, Ed Barbeau, 22:5, 1991, 403, F
Four Crotchets on Elementary Integration, Leroy F. Meyers, 22:5, 1991, 410-413, C, 5.2.3, 5.2.5, 6.1
FFF #49. Two Transcendental Equations, Ed Barbeau, 23:1, 1992, 36, F, 0.2
The Relationship Between Hyperbolic and Exponential Functions—Revisited, Roger B. Nelsen, 23:3, 1992, 207-208, C, 5.3.3
Napier's Inequality (two proofs), Roger B. Nelsen, 24:2, 1993, 165, C
FFF #58. A Rational Combination of Two Transcendentals, Ed Barbeau, 24:3, 1993, 229, F, 0.2
FFF #60. A Two-Valued Function, Ed Barbeau, 24:3, 1993, 230, F, 0.2 (also 25:3, 1994, 225)
An Alternative Definition of the Number e, Carl Swenson and Andre Yandl, 24:5, 1993, 458-461
Another Proof of the Formula e = the infinite sum of reciprocals of n!, Norman Schaumberger, 25:1, 1994, 38-39, C, 5.1.2
Riemann Sums and the Exponential Function, Sheldon P. Gordon, 25:1, 1994, 39-40, C, 5.2.1
Log Cabin (Lost at C), Paul R. Halmos, 25:1, 1994, 70, C
Proof Without Words: (a+b)/2 >SQR[ ab], Michael K. Brozinsky, 25:2, 1994, 98, C
FFF #95. The Integral of ln sin x, Russ Euler, 27:1, 1996, 44-45, F
A Visual Proof that ln(ab) = ln(a) + ln(b), Jeffrey Ely, 27:4, 1996, 304, C
FFF #115. A Double Exponential Function, Leszek Garwarecki, 28:2, 1997, 120-121, F
A Discover-e, Helen Skala, 28:2, 1997, 128-129, C
In re: e, David Fowler, 28:3, 1997, 230, C
FFF #126. The Wrong Logarithm, Eric Chandler, 29:1, 1998, 35, F (see also 30:2, 1999, 132)
When is b^e^a > a^e^b?, Norman Schaumberger, 30:4, 1999, 296, C
FFF #149. Lack of technical unanimity, Carlton A. Lane, 30:4, 1999, 306, F
FFF #158. More Log Jams, J. Sriskandarajah, 31:3, 2000, 207-208, F
Limit of (1 + 1/n)^n = e (Mathematics Without Words), Roger B. Nelsen, 32:1, 2001, 71, C
Good Rational Approximations to Logarithms, Tom M. Apostol and Mamikon Mnatsakanian, 32:3, 2001, 172-179
Mathematics Without Words: Integration of the Natural Logarithm, Roger Nelsen, 32:5, 2001, 368, C
An Elementary Approach to e^x, John W. Hagood, 32:5, 2001, 375-376, C
Why It Might Seem That Christmas is Coming Early This Year, David Strong, 32:5, 2001, 376-377, C
Ln 2 (Mathematics Without Words), Norman Schaumberger, 33:1, 2002, 23, C, 5.4.2
Hat Derivatives, Stephen B. Maurer, 33:1, 2002, 32-37, 5.1.2
Sums of Logarithms, Colonel Johnson, Jr., 33:1, 2002, 41, C
Proofs Without Words Under the Magic Curve, Fusun Akman, 33:1, 2002, 42-46, C
An Overlooked Calculus Question, Eugene Couch, 33:5, 2002, 399-400, C
A Simple Introduction to e, Pratibha Ghatage, 34:4, 2003, 323-324, C
Improving the Convergence of Newton’s Series Approximation for e, Harlan J. Brothers, 35:1, 2004, 34-39, 5.4.2
FFF #228. An exponential equation, Ed Barbeau, 35:5, 2004, 382, F, 0.2  (see also Henry J. Barten, 37:1, 2006, 42)
Placing the Natural Logarithm and the Exponential Function on an Equal Footing, Michel Helfgott, 35:5, 2004, 390-393, C
Approaching ln x, James V. Peters, 36:2, 2005, 146-147, C, 9.5
An Elementary Proof of the Monotonicity of (1+1/n)^n and (1+1/n)^(n+1), Duane W. DeTemple, 36:2, 2005, 147-149, C, 9.5
Intersections of Tangent Lines of Exponential Functions, Timothy G. Feeman and Osvaldo Marrero, 36:3, 2005, 205-208, 0.5, 5.1.3
Differentiability of Exponential Functions, Philip M. Anselone and John W. Lee, 36:5, 2005, 388-393
FFF. Logarithmic behaviour as metaphor, Norton Starr, 36:5, 2005, 394-396, F
FFF #250. Minding the technology, Paul H. Schuette, 37:2, 2006, 122-123, F, 5.3.3
An Exceptional Exponential Function, Branko Curgus, 37:5, 2006, 344-354, 5.1.4, 5.3.4
Transcendental Functions and Initial Value Problems: A Different Approach to Calculus II, Byungchul Cha, 38:4, 2007, 288-296, 5.3.1, 5.3.3, 6.1
The Convergence Behavior of fa(x) = (1 + 1/x)^(x + α), Cong X. Kang and Eunjeong Yi, 38:5, 2007, 385-387, C, 5.1.1, 9.5
Teaching Tip: An Introduction to eix without Series, James Tanton, 39:1, 2008, 23, C, 5.4.3, 6.1
FFF #280. A classic log-ical error, Dale Buske, 39:3, 2008, 229, F
FFF #287. Criticizing a critical point, Ollie Nanyes, 39:5, 2008, F, 383, 5.1.4
FFF #287. Logging the solutions of an equation, Ed Barbeau, 39:5, 2008, 383-384, F, 0.2