In order to save for college, you invested your summer savings of $2,000 into an account at the bank. The interest rate is 3.2% and the interest is compounded.

Slides:

Advertisements

Similar presentations

9.5 Exponential Equations & Inequalities. Logarithmic vocabulary Consider: log 260 Also: log 0.26 Ex 1) Underline the mantissa & circle the characteristic.

Advertisements

18 Days. Five Days  What equations did you come up with to model your data in the penny lab?

9.4 Properties of Logarithms. Since a logarithmic function is the inverse of an exponential function, the properties can be derived from the properties.

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”

6.6 – Solving Exponential Equations Using Common Logarithms. Objective: TSW solve exponential equations and use the change of base formula.

Essential Questions: 1. How do I solve exponential functions? 2. How do I solve logarmithic functions?

Warm-up 1. Convert the following log & exponential equations 1. Convert the following log & exponential equations Log equationExponential Equation Log.

EQ: How do you use the properties of exponents and logarithms to solve equations?

CONVERTING FROM ONE FORM TO ANOTHER EVALUATING PROPERTIES OF LOGS – EXPANDING AND CONDENSING Day 1:

STUDENTS WILL BE ABLE TO: CONVERT BETWEEN EXPONENT AND LOG FORMS SOLVE LOG EQUATIONS OF FORM LOG B Y=X FOR B, Y, AND X LOGARITHMIC FUNCTIONS.

11.3 – Exponential and Logarithmic Equations. CHANGE OF BASE FORMULA Ex: Rewrite log 5 15 using the change of base formula.

8.5 – Exponential and Logarithmic Equations. CHANGE OF BASE FORMULA where M, b, and c are positive numbers and b, c do not equal one. Ex: Rewrite log.

Section 3.4 Exponential and Logarithmic Equations.

8.5 – Using Properties of Logarithms. Product Property:

CHAPTER 5 SECTION 5.5 BASES OTHER THAN e AND APPLICATIONS.

Today in Pre-Calculus Go over homework Need a calculator Review Chapter 3 Homework.

7.4a Notes – Evaluate Logarithms. 1. Solve for x. a. x = 2 b. c.d. x = 1 x = 0 x = -2.

1. 2 Switching From Exp and Log Forms Solving Log Equations Properties of Logarithms Solving Exp Equations Lnx

8.3-4 – Logarithmic Functions. Logarithm Functions.

3.4 Solving Exponential and Logarithmic Equations.

Chapter 11 Section 11.1 – 11.7 Review. Chapter 11.1 – 11.4 Pretest Evaluate each expression 1. (⅔) -4 = ___________2. (27) - ⅔ = __________ 3. (3x 2 y.

Solving Logarithmic Equations

Chapter 3 Exponential and Logarithmic Functions 1.

Copyright © 2009 Pearson Education, Inc. Slide Active Learning Lecture Slides For use with Classroom Response Systems © 2009 Pearson Education, Inc.

PRE-AP PRE-CALCULUS CHAPTER 3, SECTION 3 LOGARITHMIC FUNCTIONS AND THEIR GRAPHS

Logarithms 1 Converting from Logarithmic Form to Exponential Form and Back 2 Solving Logarithmic Equations & Inequalities 3 Practice Problems.

7.4 Logarithmic Functions Write equivalent forms for exponential and logarithmic equations. Use the definitions of exponential and logarithmic functions.

3.3 Properties of Logarithms Students will rewrite logarithms with different bases. Students will use properties of logarithms to evaluate or rewrite logarithmic.

Applications of Common Logarithms Objective: Define and use common logs to solve exponential and logarithmic equations; use the change of base formula.

Precalculus – Section 3.3. How can you use your calculator to find the logarithm of any base?

3.3 Properties of Logarithms Change of base formula log a x =or.

4.5 Properties of Logarithms. Properties of Logarithms log log 6 3 log 4 32 – log 4 2 log 5 √5.

6.10/6.11 Laws of Logarithms and change of base formula.

Common Logarithms - Definition Example – Solve Exponential Equations using Logs.

Chapter 3 Exponential and Logarithmic Functions

Logarithmic Functions. Examples Properties Examples.

3.3 Logarithmic Functions and Their Graphs

Logarithmic Properties Exponential Function y = b x Logarithmic Function x = b y y = log b x Exponential Form Logarithmic Form.

Properties of logarithms. Properties of Logarithms Let b, u, and v be positive numbers such that b≠1. Product property: log b uv = log b u + log b v Quotient.

4.4 Exponential and Logarithmic Equations. Solve: 2 x = 7 3 x+3 = 5.

Lesson 9 – 5 Exponential Equations & Inequalities

8.5 – Exponential and Logarithmic Equations

Find the solution of the exponential equation, correct to four decimal places. e x =

Exponential and Logarithmic Function

8.5 – Exponential and Logarithmic Equations

You are a winner on a TV show. Which prize would you choose? Explain.

Logarithmic Functions and Their Graphs

Ch. 3 – Exponential and Logarithmic Functions

Evaluate Logarithms Chapter 4.5.

Logs on the Calculator and Solving Exponential Functions

6.4 Logarithmic & Exponential Equations

Logs – Solve USING EXPONENTIATION

Packet #15 Exponential and Logarithmic Equations

Ch 3.3: Properties of Logarithms

Sec. 5.3 Properties of Logarithms

Properties of Logarithmic Functions

Natural Logarithms - Differentiation

Solve for x: log3x– log3(x2 – 8) = log38x

4.1/4.2 – Exponential and Logarithmic Functions

bell ringer How do you “convert”?

Homework Check.

Properties of logarithms

Logarithmic Functions

Warm-up: Solve for x: CW: Practice Log Quiz HW: QUIZ Review 3.1 – 3.4.

6.3 Logarithmic Functions

Compound Interest If a principal P is invested at an interest rate r for a period of t years, then the amount A of the investment is given by A = P(1 +

Property #1 – Product Property log a (cd) =

Bell ringer The Johnson’s started a savings account for their son. They invested $5,000 in an account with a 7.5% interest rate that compounds.

Presentation transcript:

In order to save for college, you invested your summer savings of $2,000 into an account at the bank. The interest rate is 3.2% and the interest is compounded continuously for four years. Answer the following questions to the best of your knowledge: What type of function is represented by the above question? What does “compounded continuously” mean? What is the difference between compounding continuously and simple interest?

Exponential and Logarithmic Functions

Converting from log to exp. Convert to an exponential and solve

Properties of Logarithms (Very important for logarithmic differentiation) 1) 2) 3)

Ex1) Condense and write as a single log Ex2) Condense and write as a single log

Solving Logarithmic and Exponential Functions Ex1) Solve ***Change of base formula***

Ex2) Solve Ex3) Solve

Ex4) Solve Ex5) Solve

Ex6) Solve Ex7) Solve

Pg. 355 (11-33odd, 55-75odd, not 61 or 63---No calculators)