ABSTRACT
The logarithm (log) of a number has the same value as the exponent: the power to which a base must be raised so that it equals the given number.
Example 6.1 log216=4 because 24=16 Read this as ‘the log to the base 2 of 16 equals 4 because 2 to the power 4 equals 16’. Likewise, log10100=2 because 102=100
In general, then, logb a=x when bx=a Since the value of a logarithm depends on the base, this must be specified or
implied. ‘Logarithm’ is usually abbreviated to ‘log’ with the specified base as a subscript, e.g. log2. However, the most frequently encountered logs are those with base 10 (called common logs) and those with base e (called natural or Naperian logs: e being a number with a value of approximately 2.718. It is not necessary to understand how it is derived to use it.) A common log is usually written as ‘log’, and a natural log as ‘In’. This is how they appear on calculator keys. So,
log2 a specifies the base 2 whereas log a implies log10a (a common log) and In a implies logea (a natural log)
Note that any positive numbers can have logs, but zero and negative numbers cannot. What is log100? It means 10x=0 but there is no value of x for which this could be true: a positive or negative value of x gives a value greater than 0, and 100=1. What is log10(-10)? 10x=-10. Again, there is no value of x for which this could be true.
