Logarithms Revision Questions Form Two Basic Mathematics
A logarithm answers the question: How many of one number do we multiply to get another number. For example; how many of 2s do we multiply to get 16? Answer: 2 x 2 x 2 x 2= 16 so we needed to multiply 4 of the 2s to get 16. So the logarithm is 4.
How to write it?
We would write the number of 2s we need to multiply to get 16 is 4 as:
The two things are the same:
The number we are multiplying is called the base. So we can say ‘the logarithm of 16 with base 2 is 4’ or ‘log base 2 of 16 is 4’ or ‘the base-2 log of 16 is 4’.
Not that we are dealing with 3 numbers:
- The base (the number we are multiplying in our example it is 2)
- How many times to use it in multiplication (in our example it is 4 times, which is the logarithm)
- The number we want to get (in our example it is 16)
There is a relationship between the exponents and logarithms. The exponent says how many times to use the number in a multiplication and logarithm tells you what the exponent is. See the illustration below:
Generally: ax = y in logarithmic form is: LogaY = X
Example 1
write the following statements in logarithmic form:
Laws Of Logarithms
State the laws of logarithms
There are several laws of logarithms which help in evaluating them. These laws are valid for only positive real numbers. The laws are as follows:
