Download presentation

Presentation is loading. Please wait.

Published byEmmeline Johnson Modified over 8 years ago

1
Properties of Logarithms

2
The Product Rule Let b, M, and N be positive real numbers with b 1. log b (MN) = log b M + log b N The logarithm of a product is the sum of the logarithms. For example, we can use the product rule to expand ln (4x): ln (4x) = ln 4 + ln x.

3
The Quotient Rule Let b, M and N be positive real numbers with b 1. The logarithm of a quotient is the difference of the logarithms.

4
The Power Rule Let b, M, and N be positive real numbers with b = 1, and let p be any real number. log b M p = p log b M The logarithm of a number with an exponent is the product of the exponent and the logarithm of that number.

5
Text Example Write as a single logarithm: a. log 4 2 + log 4 32 Solution a. log 4 2 + log 4 32 = log 4 (2 32) Use the product rule. = log 4 64 = 3 Although we have a single logarithm, we can simplify since 4 3 = 64.

6
Properties for Expanding Logarithmic Expressions For M > 0 and N > 0:

7
Example Use logarithmic properties to expand the expression as much as possible.

8
Example cont.

10
Properties for Condensing Logarithmic Expressions For M > 0 and N > 0:

11
The Change-of-Base Property For any logarithmic bases a and b, and any positive number M, The logarithm of M with base b is equal to the logarithm of M with any new base divided by the logarithm of b with that new base.

12
Use logarithms to evaluate log 3 7. Solution: or so Example

13
Properties of Logarithms

Similar presentations

© 2024 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