Logarithms

What are logarithms?

Scales used to compress a wide range of values into a much smaller range.

What are some examples of logarithmic scales? (3)

• Richter scale

• pH scale

• Decibel scale

What is the Richter scale?

The scale used to measure the strength of an earthquake.

What is the pH scale?

A scale in chemistry used to measure the acidity of a solution.

What is the Decibel scale?

A scale used to rank the intensity of sound.

What is an exponent?

A mathematical notation indicating the number of times a quantity is multiplied by itself.

What is the common logarithm?

Log.

Log has a base of what?

10.

What is the definition of the common logarithm? (Log)

The number of tens that must be multiplied together to produce a number OR it is the exponent (power) to which 10 must be raised to produce a number. (Both of these definitions are true).

log 10

1

log 100

2

log 1000

3

log 10 000

4

log 100 000

5

log 1 000 000

6

What is a rule that can be used when determining the value of log#? (must be a multiple of 10)

Counting the number of zeros there are, will equal the answer to the log. (ie. log 100 = 2; there are 2 zeros in 100)

log 1

0

log 1/10

-1

log 1/100

-2

log 1/1000

-3

log 1/10 000

-4

log 1/100 000

-5

log 1/1 000 000

-6

What is the rule for log(1/#), particularly when the denominator is a multiple of 10?

The log of the reciprocal of the # equals the negative log of that number (ie. log 100 = 2, log 1/100 = -2)

Can Log scales be multiplied and divided?

No.

Can Log scales be added and subtracted?

Yes.

10² + 10³ = ?

2 + 3 = 5, therefore 10^5

1 000 000/10 000 = ?

log 1 000 000 - log 10 000

6 - 4

2

10² = 100