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 (ab) = \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 \lg 10 = 1\,.

In our case, we have

\displaystyle \lg 10^{3} = 3\cdot \lg 10 = 3\cdot 1 = 3\,\textrm{.}