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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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