Logarithmic Functions

Slides:

Advertisements

Similar presentations

Logarithmic Equations Unknown Exponents Unknown Number Solving Logarithmic Equations Natural Logarithms.

Advertisements

Properties of Logarithms

Table of Contents Solving Logarithmic Equations A logarithmic equation is an equation with an expression that contains the log of a variable expression.

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

6. 3 Logarithmic Functions Objectives: Write equivalent forms for exponential and logarithmic equations. Use the definitions of exponential and logarithmic.

7.6 – Solve Exponential and Log Equations

Table of Contents Solving Exponential Equations An exponential equation is an equation with a variable as part of an exponent. The following examples will.

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 logs to solve equations: Solve the following equation for t to the nearest hundredth:

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: Lesson 53. LESSON OBJECTIVE: 1)Simplify and evaluate expressions using the properties of Logarithms. 2)Solve logarithmic equations.

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.

8.3-4 – Logarithmic Functions. Logarithm Functions.

Exponentials without Same Base and Change Base Rule.

8.4 Logarithms 3/ 14 /2014. Introduction to Logarithm Video

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

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.

Exponential and Logarithmic Functions Logarithms Exponential and Logarithmic Functions Objectives Switch between exponential and logarithmic form.

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

9.5 - The Quadratic Formula

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

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

4.4 Logarithmic Functions Morgan From his TV show, what is Dexter’s last name?

Solving Logarithmic Equations

Converting between log form and exponential form.

Exponential and Logarithmic Equations

12.8 Exponential and Logarithmic Equations and Problem Solving Math, Statistics & Physics 1.

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.

Splash Screen. Example 1 Find Common Logarithms A. Use a calculator to evaluate log 6 to the nearest ten-thousandth. Answer: about Keystrokes:

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.

3.4 – Solving Exponential and Logarithmic Equations Ch. 3 – Exponential and Logarithmic Functions.

Natural Logarithms/Base e Unit 9. Definition The exponential function is called the natural exponential function and e is called the natural base.

8.4 Logarithmic Functions 4/8/2013. Definition of a Logarithmic Function log b n = p is equivalent to b p = n (logarithmic form) (exponential form)

Collins Type I What assumption(s) do you make about a population’s growth when you make predictions by using an exponential expression?

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

Review of Logarithms. Review of Inverse Functions Find the inverse function of f(x) = 3x – 4. Find the inverse function of f(x) = (x – 3) Steps.

Properties of Logarithm

6.1 - Logarithmic Functions

5.5 Solving Exponential and Logarithmic Equations

6. 3 Logarithmic Functions Objectives: Write equivalent forms for exponential and logarithmic equations. Use the definitions of exponential and logarithmic.

Lesson 6.3 Logartithms and Logarithmic Functions(Day 1)

Exponential & Logarithmic Functions

Logarithmic Functions and Their Graphs

Examples Solving Exponential Equations

Section 6.4 Properties of Logarithmic Functions Objectives:

Do Now: Determine the value of x in the expression.

Exponential and Logarithmic Equations

U6D7 Assignment, red pen, pencil, highlighter, textbook, GP notebook

Packet #15 Exponential and Logarithmic Equations

Logarithms and Logarithmic Functions

Logarithmic Functions

Write each in exponential form.

Properties of Logarithms

5A.1 - Logarithmic Functions

Logarithmic Functions

3.4 Exponential and Logarithmic Equations

Warm Up Solve for x:

4.5 Properties of Logarithms

4 minutes Warm-Up Write each expression as a single logarithm. Then simplify, if possible. 1) log6 6 + log6 30 – log6 5 2) log6 5x + 3(log6 x – log6.

6.1 - Logarithmic Functions

Logarithmic Functions

Presentation transcript:

Logarithmic Functions

Objectives Write equivalent forms for exponential and logarithmic equations. Use the definitions of exponential and logarithmic functions to solve equations.

Solve for x. 10x = 1,000 10x = 1 . 1,000 10x = 85 To solve, a logarithm is needed.

Equivalent Exponential and Logarithmic Forms For any positive base b, where b ≠ 1: bx = y if and only if x = logby.

Exponential Form Logarithmic Form 103 = 1,000 log101,000 = 3

Write in logarithmic form. 2. 1. 54 = 625

Write in exponential form 1. log100.1 = -1 2.

One-to-One Property of Exponents If bx = by, then x = y.

Find the approximate value of each logarithmic expression.

Solve each equation for x. Round to the nearest hundredth. 2. 3.

Find the value of v in each equation. 1. v = log10 0.01 2. 2 = log7 v

Find the value of v in each equation. 3. 4.

HOMEWORK Worksheet