Download presentation

Presentation is loading. Please wait.

Published byDevin Sides Modified over 3 years ago

1
**Chapter 5: Exponential and Logarithmic Functions 5**

Chapter 5: Exponential and Logarithmic Functions 5.6: Solving Exponential Logarithmic Equations Day 1 Essential Question: Give examples of equations that can be solved by using the properties of exponents and logarithms.

2
**5.6: Solving Exponential and Logarithmic Equations**

Powers of the Same Base Solve the equation 8x = 2x+1 8x = 2x+1 (23)x = 2x+1 23x = 2x+1 Set the exponents equal to each other 3x = x+1 2x = 1 x = 1/2

3
**5.6: Solving Exponential and Logarithmic Equations**

Powers of the Different Bases Solve the equation 5x = 2 5x = 2 log52 = x log 2/log 5 = x x =

4
**5.6: Solving Exponential and Logarithmic Equations**

Powers of the Different Bases Solve the equation 24x-1 = 31-x Take one base and make it into a log problem log231-x = 4x-1 (1 – x)log23 = 4x-1 (1 – x)(log 3/log 2) = 4x – 1 (1 – x)(1.5850) = 4x – 1 Calculate log 3/log 2 – x = 4x – 1 Distribute on left – x = 4x Add 1 to both sides = x Add x to both sides x = Divide by

5
**5.6: Solving Exponential and Logarithmic Equations**

Using Substitution Solve the equation ex – e-x = 4 ex – e-x = 4 Multiply all terms by ex to remove the negative exponent e2x – 1 = 4ex Set everything equal to 0, substitute u = ex e2x – 4ex – 1 = 0 u2 – 4u – 1 = 0 This is now a… Quadratic Equation

6
**5.6: Solving Exponential and Logarithmic Equations**

Using Substitution Set u back to ex, and solve

7
**5.6: Solving Exponential and Logarithmic Equations**

Assignment Page 386 Problems 1-31, odd problems Show work

8
**Chapter 5: Exponential and Logarithmic Functions 5**

Chapter 5: Exponential and Logarithmic Functions 5.6: Solving Exponential Logarithmic Equations Day 2 Essential Question: Give examples of equations that can be solved by using the properties of exponents and logarithms.

9
**5.6: Solving Exponential and Logarithmic Equations**

Applications of Exponential Equations Radiocarbon Dating The half-life of carbon-14 is 5730 years, so the amount of carbon-14 remaining at time t is given by Many of these problems will deal with percentage of carbon-14 remaining, so P = 1 (i.e. 100%), and the amount remaining will be the percentage left.

10
**5.6: Solving Exponential and Logarithmic Equations**

Applications: Carbon Dating The skeleton of a mastodon has lost 58% of its original carbon-14. When did the mastodon die? If 58% has been lost, then 42% remains

11
**5.6: Solving Exponential and Logarithmic Equations**

Applications: Compound Interest If $3000 is to be invested at 8% per year, compounded quarterly, in how many years will the investment be wroth $10,680?

12
**5.6: Solving Exponential and Logarithmic Equations**

Assignment Page 386 Problems 53-67, odd problems Show work

13
**Chapter 5: Exponential and Logarithmic Functions 5**

Chapter 5: Exponential and Logarithmic Functions 5.6: Solving Exponential Logarithmic Equations Day 3 Essential Question: Give examples of equations that can be solved by using the properties of exponents and logarithms.

14
**5.6: Solving Exponential and Logarithmic Equations**

Applications: Population Growth A culture started at 1000 bacteria. 7 hours later, there are 5000 bacteria. Find the function and when there are 1 billion bacteria. Function is based off A = Pert. Need to find r.

15
**5.6: Solving Exponential and Logarithmic Equations**

Applications: Population Growth To find A=1,000,000, need to find t

16
**5.6: Solving Exponential and Logarithmic Equations**

Solve the equation ln(x – 3) + ln(2x + 1) = 2(ln x) ln[(x – 3)(2x + 1)] = ln x2 ln(2x2 – 5x – 3) = ln x2 Natural logs cancel each other out 2x2 – 5x – 3 = x2 x2 – 5x – 3 = 0 Use quadratic equation

17
**5.6: Solving Exponential and Logarithmic Equations**

Solve the equation ln(x – 3) + ln(2x + 1) = 2(ln x) Because = , it’s undefined for ln(x – 3), so there’s only one solution

18
**5.6: Solving Exponential and Logarithmic Equations**

Equations with logarithmic & constant terms Solve ln(x – 3) = 5 – ln(x – 3) ln(x – 3) + ln(x – 3) = 5 2 ln(x – 3) = 5 ln (x – 3) = 2.5 e2.5 = x – 3 e = x x =

19
**5.6: Solving Exponential and Logarithmic Equations**

Equations with logarithmic & constant terms Solve log(x – 16) = 2 – log(x – 1) log(x – 16) + log(x – 1) = 2 log [(x – 16)(x – 1)] = 2 log (x2 – 17x + 16) = 2 102 = x2 – 17x + 16 0 = x2 – 17x – 84 0 = (x – 21)(x + 4) x = 21 or x = -4 x = -4 would give log(-4 – 16) = log -20, which is undefined There is only one solution, x = 21

20
**5.6: Solving Exponential and Logarithmic Equations**

Assignment Page 386 Problems & 69-75, odd problems Show work

Similar presentations

OK

We can unite bases! Now bases are same!. We can unite bases! Now bases are same!

We can unite bases! Now bases are same!. We can unite bases! Now bases are same!

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on 2nd world war countries Ppt on current environmental issues Ppt on perimeter and area of plane figures Ppt on world wide web Ppt on area of rectangle and square Ppt on cartesian product model Ppt on artificial intelligence in computer Ppt on world ozone day Ppt on australian continent area Ppt on 2nd world war youtube