# Logarithms%20and%20Logarithmic%20Functions - PowerPoint PPT Presentation

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## Logarithms%20and%20Logarithmic%20Functions

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### The students will solve logarithmic expressions. ( Application) (Mathematics, ... ( loge or ln) STAI 6, 23, 26. Examples. Evaluate the expression log381. 3x = 81 ... – PowerPoint PPT presentation

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Title: Logarithms%20and%20Logarithmic%20Functions

1
Logarithms and Logarithmic Functions
• Coach Baughman
• November 20, 2003
• Algebra II

STAI 3
2
Objectives
• The students will identify a logarithmic
function. (Knowledge) (Mathematics, Algebra II,
6.a)
• The students will solve logarithmic expressions.
(Application) (Mathematics, Algebra II, 6.b)
• The students will solve logarithmic functions.
(Application) (Mathematics, Algebra II, 6.c)

STAI 1, 11
3
John Napier
• Born in Edinburgh, Scotland, in 1550
• Began education at St. Andrews University at the
age of 13
• Likely acquired mathematical knowledge at the
University of Paris
• Died April 4, 1617 in Edinburgh, Scotland

STAI 7
4
Logarithms
• Definition If b and y are positive where b?1,
then the logarithm of y with base b (logby) is
defined as
• logby x
• if and only if bx y.

STAI 10
5
Special Logarithms
• logb1 0
• Why? b0 1
• logbb 1
• Why? b1 b
• The logarithm with base 10 is called the common
logarithm. (log10 or log)
• The logarithm with base e is called the natrual
logarithm. (loge or ln)

STAI 6, 23, 26
6
Examples
• Evaluate the expression log381
• 3x 81
• 3x 34
• x 4
• Evaluate the expression log1/28
• (1/2)x 8
• (1/2)x 23
• x -3
• (1/2)x (1/2)-3

STAI 4, 19, 25
7
Logarithmic Functions
• Exponential functions and logarithmic functions
are inverses
• undo each other
• If g(x) logbx and f(x) bx, then g(f(x))
logbbx x and
• f(g(x)) blogbx x.

STAI 23
8
Examples
• Simplify the expression 10log2
• 10log2 2
• Simplify the expression log39x
• log39x log3(32)x
• log332x
• 2x

STAI 4, 19, 25
9
More Examples
• Find the inverse of y log3x
• Use the definition of a logarithm
• y 3x
• Find the inverse of y ln(x 1)
• y ln(x 1)
• x ln(y 1) (switch x and y)
• ex y 1 (write in exponential form)
• ex 1 y (solve for y)

STAI 4, 19, 25
10
Assessment
1. Write log7b 13 in exponential form.
2. Write 43 64 in logarithmic form.
3. Solve the equation logx(1/32) -5.
4. Simplify log5252.
5. Evaluate log4256.
6. Find the inverse of y ln(2x 5)

STAI 25, 33, 36
11
Closing Questions
• What did we learn about today?
• Can anyone tell me the definition of a logarithm?
• Where might you use logarithms?

STAI 10, 20, 26
12
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