Logarithms, or logs for short, provide a way to extract unknown powers in an expression. When you come across logs, you will see the word ‘log’ followed by a small number that we call a subscript – this subscript is known as the ‘base’. This is followed by a number in brackets although sometimes the brackets are left out.
When reading the expressions, replace ‘log’ with ‘the power of’ and this reads as ‘the power of a to get a result of b is c’. So it is evident that this can be used interchangeably with the equation
Example – can be changed to and so x is 8.
Some students find logarithms or logs quite confusing. It can be helpful to read logs in a certain way. For instance, can be thought of as the power of a that gives b. a is known as the base of the logarithm.
For example, in the base is 2 and since it can be read as the power of 2 to give 8, the value of is 3.
Some other examples include:
since anything to the power of 0 is 1.
See more on logs:
*Quite often, in exam questions where logs are used, it is useful to use and interchangeably.