From Förberedande kurs i matematik 1

Instead of always going back to the definition of the logarithm, it is better to learn to work with the log laws,

\displaystyle \lg \left( ab \right)=\lg a+\lg b

\displaystyle \lg a^{b}=b\lg a

and to simplify expressions first. By working in this way, one only needs, in principle, to learn that \displaystyle \text{lg 1}0\text{ }=\text{1}.

In our case, we have

\displaystyle \lg 10^{3}=3\centerdot \lg 10=3\centerdot 1=3.