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Logarithms

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Logarithms AS Physics Skills Homework Complete logarithms homework sheet. Learning Objectives To learn how to use logarithms to solve equations. – PowerPoint PPT presentation

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Title: Logarithms


1
Logarithms
  • AS Physics Skills

2
Homework
  • Complete logarithms homework sheet.

3
Learning Objectives
  • To learn how to use logarithms to solve equations.

4
Logarithms
  • 100 102
  • In this statement we say that 10 is the base and
    2 is the power or index.
  • Logarithms provide an alternative way of writing
    a statement such as this. We rewrite it as
  • log10 100 2
  • This is read as log to the base 10 of 100 is 2.

5
Logarithms
6
Logarithms
  • I like to think of logba as meaning
  • what power of b is a?
  • So log1010000 translates to-
  • what power of 10 is 10,000? ? 4
  • So log327 translates to-
  • what power of 3 is 27? ? 3

7
Another Example
  • 25 32
  • we can write this as
  • log2 32 5
  • Here the base is 2 and the power is 5. We read
    this as log to the base 2 of 32 is 5.

8
e
  • e is a special number, a bit like p
  • It has the property that if you plot yex, then
    at every point on the curve the slope also equals
    the y-value
  • For example, if x5, then ye5 and the slope at
    that point, e5.
  • e 2.718281828

9
Log Rule 1
Example with Numbers-
10
Log Rule 2
  • Examples with Numbers-

11
Log Rule 3
  • Examples with Numbers-

12
Log Rules
  • Examples with Numbers-

13
Inverse Logs
  • Examples with numbers-

14
Standard Bases
  • In Science, we tend to use only two bases either
    log to the base 10, which is written as just
    log or as lg.
  • Or we use log to the base e (natural logarithm),
    which is written as ln.
  • Similarly,

15
Solving Equations
  • For example, say we want to find x for-
  • Log both sides-
  • Using log rule No.3-
  • Re-arranging-
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