Mathematics

Problem

a

b

, and

c

are consecutive positive terms of a geometric progression, which of the following relations between their common (base

10

) logarithms is always true? a)

\log_{10} a + \log_{10} b = 2\,\log_{10} c

\log_{10} a + \log_{10} c = 2\,\log_{10} b

\displaystyle \log_{10} b = \frac{\log_{10} a + \log_{10} c}{3}

\bigl(\log_{10} b\bigr)^{2}=\log_{10} a\,\log_{10} c