Download presentation

Published byAudrey Keating Modified over 4 years ago

1
4 minutes Warm-Up Solve each equation for x. Round your answers to the nearest hundredth. 1) 10x = 1.498 2) 10x = Find the value of x in each equation. 3) x = log4 1 4) ½ = log9 x

2
**6.4.1 Properties of Logarithmic Functions**

Objectives: Simplify and evaluate expressions involving logarithms Solve equations involving logarithms

3
**Properties of Logarithms**

For m > 0, n > 0, b > 0, and b 1: Product Property logb (mn) = logb m + logb n

4
**Example 1 given: log5 12 1.5440 log5 10 1.4307 log5 120 =**

5
**Properties of Logarithms**

For m > 0, n > 0, b > 0, and b 1: Quotient Property logb = logb m – logb n m n

6
**Example 2 given: log5 12 1.5440 log5 10 1.4307 12 log5 1.2 = log5**

–

7
**Properties of Logarithms**

For m > 0, n > 0, b > 0, and any real number p: Power Property logb mp = p logb m

8
**Example 3 given: log5 12 1.5440 log5 10 1.4307 log5 1254**

53 = 125 = 4 3 x = 3 = 12

9
**Practice Write each expression as a single logarithm.**

1) log2 14 – log2 7 2) log3 x + log3 4 – log3 2 3) 7 log3 y – 4 log3 x

10
Homework p.382 #13-21 odds,31,35

11
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 y)

12
**6.4.2 Properties of Logarithmic Functions**

Objectives: Simplify and evaluate expressions involving logarithms Solve equations involving logarithms

13
**Properties of Logarithms**

For b > 0 and b 1: Exponential-Logarithmic Inverse Property logb bx = x and b logbx = x for x > 0

14
Example 1 Evaluate each expression. a) b)

15
**Practice Evaluate each expression. 1) 7log711 – log3 81**

16
**Properties of Logarithms**

For b > 0 and b 1: One-to-One Property of Logarithms If logb x = logb y, then x = y

17
**Example 2 Solve log2(2x2 + 8x – 11) = log2(2x + 9) for x.**

2x2 + 8x – 11 = 2x + 9 2x2 + 6x – 20 = 0 2(x2 + 3x – 10) = 0 2(x – 2)(x + 5) = 0 x = -5,2 Check: log2(2x2 + 8x – 11) = log2(2x + 9) log2 (–1) = log2 (-1) undefined log2 13 = log2 13 true

18
**Practice Solve for x. 1) log5 (3x2 – 1) = log5 2x**

2) logb (x2 – 2) + 2 logb 6 = logb 6x

19
Homework p.382 #29,33,37,43,47,49,51,57,59,61

Similar presentations

Presentation is loading. Please wait....

OK

Clock will move after 1 minute

Clock will move after 1 minute

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google