3.5 Equation Solving & Modeling

Slides:

Advertisements

Similar presentations

8.6 Solving Exponential and Logarithmic Equations p. 501.

Advertisements

Solving Exponential Equations Using Logarithms

Questions over 4.6 HW???. 4.7 (Green) Solve Exponential and Logarithmic Equations No School: Monday Logarithms Test: 1/21/10 (Thursday)

1) log416 = 2 is the logarithmic form of 4░ = 16

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.

Take a logarithm of each side

4.6 Solve Exponential and Logarithmic Equations

8.6 Solving Exponential and Logarithmic Equations

6.4 Exponential Growth and Decay. What you’ll learn about Separable Differential Equations Law of Exponential Change Continuously Compounded Interest.

8 – 6 Solving Exponential and Logarithmic Equations Day 1 Objective: Solve exponential equations.

a) y = 3 x b) y = -3 x c) y = (1/2) x d) y = -(1/2) x.

2 pt 3 pt 4 pt 5pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2pt 3 pt 4pt 5 pt 1pt 2pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4pt 5 pt 1pt Fascinating Exponential Functions.

Logarithmic Functions. Example1. On the Richter Scale, the magnitude R of an earthquake of intensity I is given by where I 0 is a certain minimum intensity.

Differential Equations Copyright © Cengage Learning. All rights reserved.

Natural Logarithms Section 5.6. Lehmann, Intermediate Algebra, 4ed Section 5.6Slide 2 Definition of Natural Logarithm Definition: Natural Logarithm A.

Today in Precalculus Go over homework Notes: Common and Natural Logarithms Homework.

Y = 10 x y = log 10 x y = x The log 10 x (pronounced log base 10) is called the inverse function of y = 10 x. The inverse function is always a reflection.

Date: 3.5 Equation Solving and Modeling (3.5) One-to-One Properties For any exponential function f(x) = b x : If b u = b v, then u = v For any logarithmic.

How are you all doing? Any questions about anything?

5.4 Logarithmic Functions. Quiz What’s the domain of f(x) = log x?

EXAMPLE 2 Take a logarithm of each side Solve 4 = 11. x 4 = 11 x log 4 = log 11 x 4 4 log 4 x = 11 x = log 11 log 4 x 1.73 SOLUTION Write original equation.

4.7 (Green) Solve Exponential and Logarithmic Equations No School: Monday Logarithms Test: 1/21/10 (Thursday)

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.

3.3 Logarithmic Functions and Their Graphs

7.6A Solving Exponential and Logarithmic Equations Algebra II.

Exponential and Logarithmic Functions 4 Copyright © Cengage Learning. All rights reserved.

Topic 10 : Exponential and Logarithmic Functions Solving Exponential and Logarithmic Equations.

LOGARITHMIC AND EXPONENTIAL EQUATIONS LOGARITHMIC AND EXPONENTIAL EQUATIONS SECTION 4.6.

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.

Algebra The Natural Base, e. Review Vocabulary Exponential Function–A function of the general form f(x) = ab x Growth Factor – b in the exponential.

Aim: What is the logarithms?

Lesson 6.6 Solving Exponential and Logarithmic Equations Day 2

Ch. 8.5 Exponential and Logarithmic Equations

Solving Exponential and Logarithmic Equations

Warm Up WARM UP Evaluate the expression without using a calculator.

Logarithmic Functions and Their Graphs

5.3 Logarithmic Functions & Graphs

22. $5,000e(0.069)(5) = $7, $20,000e(0.0375)(2) = $21, $2,000e(0.051)(3) = $2, $950e(0.06)(10) = $1, =

7.5 – Properties of Logarithms

4.2 Logarithms.

Exponential and Logarithmic Equations

Chapter 5 Logarithmic Functions.

5.4 Logarithmic Functions and Models

8.6 Solving Exponential and Logarithmic Equations

8.6 Solving Exponential and Logarithmic Equations

Day “35” Solving Exponential and Logarithmic Equations

Solving Exponential & logarithmic Equations

7.6 Solve Exponential and Logarithmic Equations

Warm-Up Find the inverse of each function. f(x) = x + 10 g(x) = 3x

Worksheet Key 1/2/2019 9:28 PM Solving Exp and Log Equations.

Equation Solving and Modeling

Differential Equations

WARMUP Lesson 7.6, For use with pages

Logarithmic and Exponential Equations

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

Equation Solving and Modeling

4.3 Logarithmic Functions

8.6 Solving Exponential and Logarithmic Equations

Exponential Functions Intro. to Logarithms Properties of Logarithms

Aim: What is the logarithms?

Logarithmic and Exponential Equations

Logarithmic Functions

Logarithmic Functions

Section 6.6 Solving Exponential and Logarithmic Equations

Properties of Logarithmic Functions

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.

College Algebra: Lesson 3

5.6 - Solving Logarithmic and Exponential Equations

Section 5.5 Additional Popper 34: Choice A for #1 – 10

MATH 1310 Section 5.3.

Presentation transcript:

3.5 Equation Solving & Modeling

One-to-One Properties For any exponential function f(x) = bx, If bu = bv, then u = v For any logarithmic function f(x) = logbx, If logb u = logb v, then u = v

Find the exact solution algebraically

You Try! Find the exact solution algebraically 2(5)

Find the exact solution algebraically

You Try! Solve:

Solve:

You Try! Solve:

Solve: ln(x-3) + ln(x+4) = 3 ln 2

You Try! Solve: log(x-2) + log(x+5) = 2 log 3

Comparing Earthquakes: How many times more severe was the 1978 Mexico City earthquake (R = 7.9) than the 1994 Los Angeles (R= 6.6)?

Newton’s Law of Cooling T(t) = Tm + (T0 – Tm)e-kt Tm = the temperature of the surrounding medium T0 = initial temperature of the object

Newton’s Law of Cooling: A cup of coffee has cooled from 920C to 500C after 12 minutes in a room at 220C. How long will the cup take to cool to 300C?