Mathematics

Problem

Consider the three non-zero numbers

3x,\; 6,\; \dfrac{12}{x}

. a. (i) Determine all real values of

x

for which these numbers, in the stated order, form a geometric progression. b. (ii) For each admissible value of

x

, verify that

\log_{10}(3x),\; \log_{10} 6,\; \log_{10}\Bigl(\dfrac{12}{x}\Bigr)

form an arithmetic progression.