Question

Determine the value of log(1000).

Answer 1

Hint: Use of logarithm formulae and properties.

Here, we have been given with log1000. Since, the base of logarithm is not mentioned we will consider the base as 10 and can rewrite it as
${\log }_{10}1000\to (1)$
As, we know that 1000 can be represented as ${10}^3$. Therefore equation (1) can be written as
${\log }_{10}{10}^3\to (2)$
Since, we know the property of logarithm i.e. ${\log }_x{a}^n=n{\log }_{x}a$. So applying the property on equation (2), we get
$\Rightarrow {\log }_{10}{10}^3=3{\log }_{10}10=3[\because {\log }_{10}10=1]$
Therefore the value of log1000 is 3.

Note: The logarithm with base 10 is called common logarithm and hence the value of base is considered as 10 if the value of base is not mentioned.