Unit 5 – Section 1 “Solving Logarithms/Exponentials with Common Bases”

Slides:

Advertisements

Similar presentations

WARM - UP. SOLVING EXPONENTIAL & LOGARITHMIC FUNCTIONS SECTION 3.4.

Advertisements

Aim: How do we solve exponential and logarithmic equations ? Do Now: Solve each equation: a. log 10 x 2 = 6 b. ln x = –3 Homework: Handout.

Section 3.4. Solving Exponential Equations Get your bases alike on each side of the equation If the variable is in the exponent set the exponents equal.

Logarithmic and Exponential Equations

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”

Logarithmic Functions

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

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

Section 4.1 Logarithms and their Properties. Suppose you have $100 in an account paying 5% compounded annually. –Create an equation for the balance B.

Properties of Logarithms Section 6.5 Beginning on page 327.

Algebra II w/trig. A logarithm is another way to write an exponential. A log is the inverse of an exponential. Definition of Log function: The logarithmic.

Warm up. 3.4 Solving Exponential & Logarithmic Equations Standards 13, 14.

6.3A – Logarithms and Logarithmic Functions Objective: TSW evaluate logarithmic expressions.

Academy Algebra II/Trig 6.6: Solve Exponential and Logarithmic Equations Unit 8 Test ( ): Friday 3/22.

Solving Exponential and Logarithmic Equations Section 8.6.

 If m & n are positive AND m = n, then  Can solve exponential equation by taking logarithm of each side of equation  Only works with base 10.

Solving Exponential and Logarithmic Equations Section 6.6 beginning on page 334.

Unit 5: Modeling with Exponential & Logarithmic Functions Ms. C. Taylor.

6.4 – Solving Logarithmic Equations and Inequalities Objective: TSW solve logarithmic equations and inequalities.

8.3-4 – Logarithmic Functions. Logarithm Functions.

Solving Logarithmic Equations To solve today's equations, we are going to rewrite them in exponential form and use the methods learned in the last unit.

Exponentials without Same Base and Change Base Rule.

5.5Logarithms Objectives: I will be able to…  Rewrite equations between exponential and logarithmic forms  Evaluate logarithms  Solve logarithms.

Do Now (7.4 Practice): Graph. Determine domain and range.

Section 9.3 Logarithmic Functions  Graphs of Logarithmic Functions Log 2 x  Equivalent Equations  Solving Certain Logarithmic Equations 9.31.

10.2 Logarithms and Logarithmic Functions Objectives: 1.Evaluate logarithmic expressions. 2.Solve logarithmic equations and inequalities.

Log Introduction  Video  **** find*****. 8.3 Lesson Logarithmic Functions.

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

5.3 Intro to Logarithms 2/27/2013. Definition of a Logarithmic Function For y > 0 and b > 0, b ≠ 1, log b y = x if and only if b x = y Note: Logarithmic.

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

Exponential and Logarithmic Functions.

Solving Exponential Equations. We can solve exponential equations using logarithms. By converting to a logarithm, we can move the variable from the exponent.

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.

10.1/10.2 Logarithms and Functions

5.5Logarithms. Objectives: I will be able to…  Rewrite equations between exponential and logarithmic forms  Evaluate logarithms  Solve logarithms Vocabulary:

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

Solving Logarithmic Equations

Converting between log form and exponential form.

MBF3C Lesson #5: Solving Exponential Equations.  I can solve an exponential equation by getting a common base.

Radical expressions, rational exponents and radical equations ALGEBRA.

8.3 – Logarithmic Functions and Inverses. What is a logarithm? A logarithm is the power to which a number must be raised in order to get some other number.

Exponents – Logarithms xy -31/8 -2¼ ½ xy 1/8-3 ¼-2 ½ The function on the right is the inverse of the function on the left.

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

Jeopardy $100 Facts About Logarithms Exponentials to Logs Evaluating Logs Expanding Logs Condensing Logs $200 $300 $200 $100 $300 $200 $100 $400 $300 $200.

Homework Questions. LOGS Warm-up Evaluating Logs.

LOGARITHMIC AND EXPONENTIAL EQUATIONS LOGARITHMIC AND EXPONENTIAL EQUATIONS SECTION 4.6.

Goals:  Understand logarithms as the inverse of exponents  Convert between exponential and logarithmic forms  Evaluate logarithmic functions.

LOGARITHMIC FUNCTIONS. LOG FUNCTIONS Exact Values Find the exact value of log 3 81 log 3 81 = x 3 x = 81 3 x = 3 4 x = 4 1.Set the equation equal to.

Understanding Exponents

Ch. 8.5 Exponential and Logarithmic Equations

6.1 - Logarithmic Functions

Solving Exponential and Logarithmic Equations

Logarithmic Functions

8.6 Solving Exponential & Logarithmic Equations

Unit 8 [7-3 in text] Logarithmic Functions

Warm-Up! Log6 x + Log6 9 = Log6 54 Log4 (x-3) + Log4 (x+3) = 2.

7.5 Exponential and Logarithmic Equations

Logarithms and Logarithmic Functions

Logarithmic Functions

Homework Questions.

Exponential and Logarithmic Equations

5A.1 - Logarithmic Functions

Homework Questions.

Warmup Solve 256

Keeper #39 Solving Logarithmic Equations and Inequalities

6.1 - Logarithmic Functions

7.4 Exponential & Logarithmic Equations

Logarithmic Functions

Presentation transcript:

Unit 5 – Section 1 “Solving Logarithms/Exponentials with Common Bases” Objectives: To write and evaluate logarithmic expressions

Writing and Evaluating Logarithmic Expressions Logarithm: 𝑦= 𝑏 𝑥  𝑙𝑜𝑔 𝑏 𝑦=𝑥 𝑙𝑜𝑔 𝑏 𝑦= “log base b of y.” Directions: Write each expression in logarithmic form. 729= 3 6 32= 2 5 1 8 = 1 2 3 10 0 =1

Evaluating Logarithms Steps: Convert to exponential form. Change each side to the same base proportionally. Set exponents equal to each other. Solve. 𝑦= 𝑏 𝑥  𝑙𝑜𝑔 𝑏 𝑦=𝑥 Directions: Evaluate each logarithm. 𝑙𝑜𝑔 8 (16) 𝑙𝑜𝑔 64 ( 1 32 ) 𝑙𝑜𝑔 9 (27) 𝑙𝑜𝑔 10 (100) 𝑙𝑜𝑔 3 (81)

Practice with Logarithms Directions: Rewrite each logarithm as an exponential form. 𝑙𝑜𝑔 13 1=0 𝑙𝑜𝑔 3 3=1 𝑙𝑜𝑔 4 64=3 𝑙𝑜𝑔 4 𝑣=𝑢 Directions: Rewrite each exponential form as a logarithm. 𝑦 2 =𝑥 16 2 =256 20 −2 = 1 400 𝑎 −1 =𝑏 Directions: Evaluate each expression. 𝑙𝑜𝑔 3 1 𝑙𝑜𝑔 7 343 𝑙𝑜𝑔 2 32 𝑙𝑜𝑔 1 7 1 49 𝑙𝑜𝑔 9 1 81

Homework Assignment Announcements