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Small World, Isn’t It? Charlotte, Samantha, Alyssa, and Amelie
Linear Stuff General form: Rate of change is “a”
Average vs. Instantaneous Instantaneous rate of change = derivative Secant lineTangent line
Derivative Approximate derivative calculation Calculating derivative The derivative of the function f(x) at a point (a, f(a)) is equal to the instantaneous rate of change of f(x) at x = a.
Exponents General form: Rules of Exponents -
Proportionality Constant General form: The derivative of an exponential function can be expressed by the proportionality constant multiplied by the function itself.
e Equal to approximately is the function where the proportionality constant is equal to 1
Logarithms Logarithms always involve non-negative bases
Change of Base Take the logarithm of both sides Divide both sides by log7
Solving Logarithmic Equations Chapter 8.6. log with same base on both sides Use this property for logarithms with the same base: log b x = log b y if.
The Nature of Exponential Growth Writing growth and decay problems with base e.
Property of Logarithms If x > 0, y > 0, a > 0, and a ≠ 1, then x = y if and only if log a x = log a y.
Objectives Solve exponential and logarithmic equations and equalities. Solve problems involving exponential and logarithmic equations.
Exponentials without Same Base and Change Base Rule.
4.4 Solving Exponential and Logarithmic Equations.
Warm-Up Simplify 4 minutes 1) 2) 3) 4). 4.1 Exponents Objectives: To multiply numbers in exponential form To divide numbers in exponential form To simplify.
Goals: Understand logarithms as the inverse of exponents Convert between exponential and logarithmic forms Evaluate logarithmic functions.
Exponents power base exponent. Warm-Up Find the value of each expression. 1.) 5 – ) (5 – 1) 3 3.) 4 (3 + 2) 4.) 10 ÷ 2 – 3 5.) 10 + (2 + 4) ÷ 4.
SECTION 5.6 Logarithmic and Exponential Equations.
Solving Proportions, Using Exponents. Proportions Many chemistry problems deal with changing one variable and measuring the effect on another variable.
Exponents base exponent means 3 factors of 5 or 5 x 5 x 5.
Exponential and Logarithmic Equations. 1. Solve each exponential equation by expressing each side as a power of the same base and then equating exponents.
7.2 Powers of 10 and Scientific Notation Pg. 452.
LOGS EQUAL THE The inverse of an exponential function is a logarithmic function. Logarithmic Function x = log a y read: “x equals log base a of y”
Essential Question: What is the first step for simplifying an exponential expression that contains negative exponents?
Page #22-25, ) a)(f+g)= 2x 2 +6 b) (f-g)= -4x 2 -4 c) (fg)= -3x 4 -2x 2 +5 d) (f/g)= (1-x 2 )/(3x 2 +5) 23) a)(f+g)= 3-2x b) (f-g)= 6x-3.
Section 5.5 Solving Exponential and Logarithmic Equations Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.
Exponents Power base exponent means 3 factors of 5 or 5 x 5 x 5.
Properties of Exponents. Product of Powers To multiply terms with the same base, add the exponents. Example: 7 3 x 7 8 = = 7 11.
WHEN MULTIPLYING LIKE BASES, YOU ADD THE EXPONENTS FOR EXAMPLE: NOW YOU TRY:
Exponents. 6³ Exponent Base 6³ is read “Six Cubed” 6³ = 6 x 6 x 6 6³ = 216.
8.4 Logarithms p The inverse of an exponential function is a logarithmic function. Logarithmic Function x = log b y read: “x equals log base b.
Logarithms Converting from Logarithmic Form to Exponential Form and Back Solving Logarithmic Equations & Inequalities Practice Problems.
EXAMPLE 2 Evaluate exponential expressions a. 6 – Product of a power property = 6 0 Add exponents. = 1 Definition of zero exponent = 6 –
Lesson 10.2Logarithmic Functions Logarithm: Inverse of exponential functions. “log base 2 of 6” Ex: Domain: x>0 Range: all real numbers Inverse of exponential.
Essential Question: What are some of the similarities and differences between natural and common logarithms.
Unit 9. Unit 9: Exponential and Logarithmic Functions and Applications.
ISP 121 Logarithms. What is a Logarithm? A logarithm (or log) is a number that represents a power or exponent Why use logs? –A simpler way to express.
Moving from Average Rate of Change (AROC) to Instantaneous Rate of Change (IROC) Today you will use the average rate of change to find the instantaneous.
Opener Evaluate when x = 4.. Test Review Simplifying Exponent Rules.
A) b) c) d) Solving LOG Equations and Inequalities **SIMPLIFY all LOG Expressions** CASE #1: LOG on one side and VALUE on other Side Apply Exponential.
Section 3.4 Exponential and Logarithmic Equations.
3.3 Day 1 Properties of logarithms –Use the product rule. –Use the quotient rule. –Use the power rule. –Expand logarithmic expressions. Pg. 407 # 2-36.
4.7 (Green) Solve Exponential and Logarithmic Equations No School: Monday Logarithms Test: 1/21/10 (Thursday)
Unit 5: Logarithmic Functions Inverse of exponential functions. Ex 1: Domain: Range: Domain: Range: Ex 2:
Unit 5: Logarithmic Functions Inverse of exponential functions. “log base 2 of 6” Ex 1: Domain: all real numbers Range: y > 0 “log base b of x” Domain:
Equality and Inequality Meeting 4. Equations An equation is a statement that two mathematical expressions are equal. The values of the unknown that make.
7-3: Rational Exponents. For any nonnegative number, b ½ = Write each expression in radical form, or write each radical in exponential form ▫81 ½ = =
Section 2.1 The Derivative Calculus for Business, Economics, the Social and Life Sciences Copyright © The McGraw-Hill Companies, Inc. Permission required.
Solving Exponential and Logarithmic Equations Section 6.6 beginning on page 334.
Exponents. Definition: Exponent The exponent of a number says how many times to use that number in a multiplication. It is written as a small number to.
Holt Algebra Exponential and Logarithmic Equations and Inequalities Solve exponential and logarithmic equations and equalities. Solve problems involving.
Linear Inequalities By Dr. Carol A. Marinas. Solving Linear Equations Linear Equations have no exponents higher than 1 and has an EQUAL SIGN. To solve.
Copyright © 2009 Pearson Education, Inc. CHAPTER 5: Exponential and Logarithmic Functions 5.1 Inverse Functions 5.2 Exponential Functions and Graphs 5.3.
Exponents Exponential Form base exponent means the product of 3 factors of 5 = 5 x 5 x 5.
Properties Power Rule: Exponential Equations Equations with variables in the exponents are called Exponential Equations For simple equation, use the.
Solving Exponential and Logarithmic Equations Section 8.6.
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