From Förberedande kurs i matematik 1

The two terms can be combined into one logarithmic expression using the log law \displaystyle \lg a + \lg b = \lg (ab),

\displaystyle \lg 23 + \lg\frac{1}{23} = \lg \Bigl(23\cdot\frac{1}{23}\Bigr) = \lg 1 = 0\,\textrm{.}