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.
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