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Logarithms

- AS Physics Skills

Homework

- Complete logarithms homework sheet.

Learning Objectives

- To learn how to use logarithms to solve equations.

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.

Logarithms

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

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.

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

Log Rule 1

Example with Numbers-

Log Rule 2

- Examples with Numbers-

Log Rule 3

- Examples with Numbers-

Log Rules

- Examples with Numbers-

Inverse Logs

- Examples with numbers-

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,

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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