## Logarithms

The common or base-10 logarithm of a number is the power to which 10 must be raised to give the number. That is, the logarithm of 100 is 2, since

100 = 10(^2), where (^) is used to indicate a superscript.

This is written as

Log(100) = 2.

Note that numbers less than one have negative logarithms:

Log (0.001) = -3 because 0.001 = 10(^-3)

Logarithms are not defined for negative numbers.

Make sure that you can reproduce the following table with your calculator. Notice that logarithms are not necessarily integers.

```N		N as a power of 10	Log(10)
1000		10(^3)			3
100		10(^2)			2
75		10(^1.875)		1.875
10		10(^1)			1
5		10(^0.699)		0.699
1		10(^0)			0
0.1		10(^-1)			-1
0.001		10(^-3)			-3
0.006		10(^-2.222)		-2.222
```

Your calculator should have a button marked LOG that you can use to obtain these logarithms

The opperation that is the logical reverse of taking a logarithm is called taking the antilog of a number. The antilog of a number is the result obtained when you raise 10 to that number.

The antilog of 2 is 100 because 10(^2) = 100.
The antilog of -2 is 0.01 because 10(^-2)= 0.01.

Your calculator will have a button such as LOG(^-1) or 10(^x) to be used for antilogs.

Make sure that you can reproduce the following table with your calculator.

```N		antilog(N)		as a power of 10
2		100			10(^2)
1.5		31.62			10(^1.5)
1		10			10(^1)
0		1			10(^0)
-2		0.01			10(^-2)
-3.4		0.0003981		10(^-3.4)
```