If is a positive number different from 1

MATHEMATICS · Single correct · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

x

is a positive number different from 1, such that

\log_a x

\log_b x

and

\log_c x

are in AP, then (1)

\log b = \frac{2(\log a)(\log c)}{(\log a + \log c)}

(2)

b = \frac{a + c}{2}

(3)

b = \sqrt{ac}

(4)

c^2 = (ac)^{\log_a b}