MAT129 Fall 2025 Notes mathnstuff.com/math/precalc/MAT129fa25/p.10.htm © 2025   A2, Agnes Azzolino Exponential and Logarithmic Functions. Text 6.1-6.4, PG. 464, 479, 491, 499

A Log Is An Exponent   Raise A Number to a Power, bx. Rewrite a fraction as a decimal. b =   x = =   Take the log, base b, of N, logb(N) b =   N = =

Welcome to Precalc! A Log Is An Exponent Hi,     This is really important stuff. This is how growth and decay happen in the real world. The computation looks messy, but it follows the rules of exponents learned in algebra. To "raise to a power" and to "take a root" are inverse functions, one undoes the other. In algebra, you learned y = mx, y = x + x + x + x, ..., + x, m times.     This is called a linear function . In precalc, you learn y = xm, y = x (x)(x)(x) ... (x), m times.     This is called a power function. Now in precalc, you learn y = mx, y = m(m)(m)(m) ... (m), x times.     This is called an exponential function.     The number e is most often the base that is used. Learn the difference between compounding in different (discrete) time periods and compounding continuously.     Contact me through the pink box on www.mathnstuff.com/math/math.htm or with the phone number on your class CANVAS home page.     Stay safe, A2

This Class Notes:	 log con-dots, exponent con-dots,  simplify con-dots, exponent laws,  blank 1 graph paper, blank 2 graph paper, 
Next Class Notes:	solve
6.1  - Exponential Functions, pg. 464,  Learning Objectives
	* Evaluate exponential functions.
	* Find the equation of an exponential function.
	* Use compound interest formulas.
	* Evaluate exponential functions with base e.
6.2  - Graphs of Exponential Functions, pg. 479,  Learning Objectives
	* Graph exponential functions.
	* Graph exponential functions using transformations.
6.3  - Logarithmic Functions, pg. 491,  Learning Objectives
	* Convert from logarithmic to exponential form.
	* Convert from exponential to logarithmic form.
	* Evaluate logarithms.
	* Use common logarithms.
	* Use natural logarithms.
6.4  - Graphs of Logarithmic Functions, pg. 499,  Learning Objectives
	* Identify the domain of a logarithmic function.
	* Graph logarithmic functions.

Log & Exponential Functions

powers of 10 3. Raise to a Power 4. Log -- Exponent base 10 the exponential function vs. an exponential function 80 math functions Notes Vocabulary Exponent & Log Laws Function Library Exponential or Power Functions     A Bit about e, the base of the Natural Logs     Linear vs Exponential Growth Compounding - Growing Discretely, WHY THE FORMULA P(t) = P0(1 + r/n)nt Even More About e, the base of the Natural Logs     Questions on exponents and logs:       graphing exponentials       Solving exponential equations Exponential and Natural Log Are Inverse Functions Logs without Feeling Out on A Limb Table of Contents Page Log Graph Papers Games:   Who Has? Exponential PRINT THESE FILES FOR USE IN TODAY'S CLASS Logarithm Connect-the-Dots pdf, or p.10.a.gif Exponent Connect-the-Dots pdf, or p.10.c.gif Expand or simplify the log pdf, or p.10.b.gif Forms Web Pages -- Dynamic Computation A Program/Web Page which Permits One to "Solve" for e EXPONENTIAL or POWER FUNCTIONS Linear vs Exponential Growth Parent Functions, Their Slope Functions, and Area Functions

Function and Relation Library Use browser to return from these Exponential or Power Functions A Bit about e, the base of the Natural Logs     Even More About e, the base of the Natural Logs     The Exponential Function     Linear vs Exponential Growth         Parent Functions, Their Slope Functions, and Area Functions

Spread Sheets -- Dynamic Computation exp.xlsx -- compound & continuous interest, logistic curve, Gaussian (Normal Statistical curve), ...

Sketch Pads -- Dynamic Analytic Geometry Transendentals, Exponentials, Logs 2graphs.gsp  -- 2 graphed functions ready to edit logs -- 1 - ln(x), e^x, y=x for inverse, 2 - 2 graphs, 3 - a(base)^(bx-c)+d, 4 -e by area under 1/x Dere2x -- Derivative of the exponential Derlnx -- Derivative of the Natural Log e2xSums -- The Antiderivative of ex