With the concentration served as an exact power of ten, the log costs nothing: $[\mathrm{H^+}] = 1 \times 10^{-3}\ \mathrm{mol/L}$ has pH 3 — read the exponent, drop its minus, done. That flip is the whole machine: $\mathrm{pH} = -\log[\mathrm{H^+}]$, and the leading minus exists precisely so everyday acids land on a POSITIVE scale.

The resident trap is that minus sign. Forget it and pH 3 becomes −3, which would out-acid anything in a school stockroom — if your pH comes out negative on this paper, the sign slipped; go back one line. And a pH carries no unit: the logarithm strips the mol/L on the way through.