Logarithm properties in aptitude – UGC NET Question

Statements A and B correctly capture fundamental logarithm values, D states the power rule and E refers to the change of base formula where one logarithm can be expressed as a constant multiple of another base’s logarithm. All of these are true. Statement C is false because the product rule for logarithms is logₐ(xy) = logₐ(x) + logₐ(y), not the difference. Therefore, the combination that includes A, B, D and E while excluding C is the only correct option.

Option A:
Option A is incomplete because although A, B and D are true, it leaves out E, which is an important fact about changing bases and is useful in more complex aptitude questions involving logarithms. The omission makes the set incomplete.

Option B:
Option B is also incomplete as it omits D, thereby ignoring the power rule, which is frequently used to simplify expressions like logₐ(xᵏ) in exam problems. Without D, the description of key log properties is not full.

Option C:
Option C is wrong because it excludes A and thereby omits the basic fact that logₐ(1) = 0, while still including the true D and E. Although some statements are correct, the absence of A means the option does not gather all true statements.

Option D:
Option D is correct because it retains all valid properties and discards the incorrect product rule in C, aligning with the standard set of logarithm rules that a NET candidate is expected to know.