2022 · Q22
If (log₁₀a)/(b-c)=(log₁₀b)/(c-a)=(log₁₀c)/(a-b), (a ≠ b ≠ c), then what is the value of abc?
Elementary MathematicsAlgebra
- A-1
- B0
- C1
- D3
Explanation
Writing each ratio as k: log a = k(b−c), log b = k(c−a), log c = k(a−b). Adding gives log a + log b + log c = 0, so log(abc) = 0 and abc = 1. The keyed option is C.