Download presentation

1
**Logarithmic Functions**

Section 4.2 Part 1 Logarithmic Functions Objectives: Change from logarithmic to exponential form. Change from exponential to logarithmic form. Evaluate logarithms. Use basic logarithmic properties.

2
**Definition of a Logarithmic Function**

For x > 0 and b > 0, b = 1, y = logb x is equivalent to by = x. The function f (x) = logb x is the logarithmic function with base b.

3
**Location of Base and Exponent in Exponential and Logarithmic Forms**

Logarithmic form: y = logb x Exponential Form: by = x. Exponent Exponent Base Base

4
**Practice #1 Write each equation in its equivalent exponential form.**

a. 2 = log5 x b. 3 = logb 64 c. log3 7 = y

5
**With the fact that y = logb x means by = x,**

Solution With the fact that y = logb x means by = x, a. 2 = log5 x means 52 = x. Logarithms are exponents. b. 3 = logb 64 means b3 = 64. Logarithms are exponents. c. log3 7 = y or y = log3 7 means 3y = 7.

6
Practice #2 Evaluate a. log2 16 b. log c. log25 5 Solution

7
**First, rewrite each expression as a logarithmic equation and convert **

Solution First, rewrite each expression as a logarithmic equation and convert to an exponential equation. Logarithmic Equation Exponential Equation Question Needed for Evaluation Evaluation a. log216 = x 2x = 16 2 to what power is 16? 4 b. log39 = x 3x = 9 3 to what power is 9? 2 c. log255 = x 25x = 5 25 to what power is 5? Since you must take the square root of 25 to get 5, that is the same as an exponent of ½. The answer is ½ .

8
**Basic Logarithmic Properties Involving One**

logb b = 1 because 1 is the exponent to which b must be raised to obtain b. (b1 = b). logb 1 = 0 because 0 is the exponent to which b must be raised to obtain 1. (b0 = 1).

9
**Inverse Properties of Logarithms**

For x > 0 and b 1, logb bx = x The logarithm with base b of b raised to a power equals that power. b logb x = x b raised to the logarithm with base b of a number equals that number.

10
Practice #3 a. log1111 b. log446 c.

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