Since $\log a, \log b,$ and $\log c$ are in A.P., we have the standard A.P. relation: $2 \log b = \log a + \log c$.

Using the power and product properties of logarithms: $\log (b^2) = \log (ac)$.

By taking the antilog on both sides (since the log function is one-to-one): $b^2 = ac$.

This is the precise defining condition for $a, b,$ and $c$ to be in Geometric Progression (G.P.).