Question

Answer the following:

If `log (("a" + "b")/2) = 1/2(log"a" + log"b")`, then show that a = b

Answer 1

`log (("a" + "b")/2) = 1/2(log"a" + log"b")`

∴ `2 log (("a" + "b")/2)` = log a + log b

∴ `log (("a" + "b")/2)^2` = log ab

∴ `("a" + "b")^2/4` = ab

∴ a² + 2ab + b² = 4ab

∴ a² + 2ab – 4ab + b² = 0

∴ a² – 2ab + b² = 0

∴ (a – b)² = 0

∴ a – b = 0

∴ a = b