From Förberedande kurs i matematik 1

If we compare the equality which defines \displaystyle \mathop{\text{lg}} 1\,,

\displaystyle 10^{\mathop{\text{lg}} 1} = 1\,,

with

\displaystyle 10^{0} = 1

we see that \displaystyle \mathop{\text{lg}} 1 = 0\,.