Chapter 7. 19. Glencoe Algebra 2. 7-3 Study Guide and Intervention. Logarithms and Logarithmic Functions. Logarithmic Functions and Expressions. Defin...
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7-3 Study Guide and Intervention Logarithms and Logarithmic Functions Logarithmic Functions and Expressions Definition of Logarithm with Base b
Let b and x be positive numbers, b ≠ 1. The logarithm of x with base b is denoted log ! 𝑥 and is defined as the exponent y that makes the equation b ! = x true.
The inverse of the exponential function y = 𝑏 ! is the logarithmic function x = 𝑏 ! . This function is usually written as y = log ! 𝑥.
Example 1: Write an exponential equation equivalent to 𝐥𝐨𝐠 𝟑 243 = 5. 3! = 243
𝟏
Example 2: Write a logarithmic equation equivalent to 𝟔!𝟑 = 𝟐𝟏𝟔. log !
!
!"#
= –3
Example 3: Evaluate 𝐥𝐨𝐠 𝟖 16. !
!
8! = 16, so log ! 16 = . !
Exercises Write each equation in exponential form. 1. log!" 225 = 2
2. log !
! !"
= –3
3. log ! 32 =
Write each equation in logarithmic form. 4. 2! = 128
7. 7!! =
!
5. 3!! =
!
6.
!"
! ! !
=
! !
! !"!
!
8. 2! = 512
9. 64! = 16
10. log ! 64
11. log ! 64
12. log!"" 100,000
13. log ! 625
14. log !" 81
15. log !" 5
17. log!" 0.00001
18. log !
!"
Evaluate each expression.
16. log !
! !"#
Chapter 7
19
! !"
Glencoe Algebra 2
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Write each equation in exponential form. 1. log ! 243 = 5 3. log ! 3 =
2. log ! 64 = 3
!
4. log !
!
!
= –2
!"
Write each equation in logarithmic form. 5. 2! = 8
