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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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