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.

Some calculators (especially business models) have only *natural*
logarithms. These can be used to obtain base-10 logarithms and
antilogs. Click here to read about
this conversion.

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)