Logarithm laws and domain preservation

Logarithm laws and domain preservation

Use logarithm laws with their hypotheses intact. This precalculus practice explains why multiplication becomes addition, division becomes subtraction and powers become coefficients, while checking where every transformed expression is defined.

Expand products and quotients, combine several rules in one expression and use absolute values when an even power permits a negative input. Analyze products of negative factors and a quotient containing a squared factor. Proof-step and counterexample questions expose the false idea that a logarithm distributes over addition.

Prerequisites include logarithm meaning, exponent rules, rational powers and basic mathematical reasoning. The single-select and multiselect tasks develop from straightforward expansion to sign-sensitive arguments and explanations of validity. No calculator is needed, and the prompt states the domain whenever a rule requires it.

Before expanding, identify the original positive argument and any denominator restrictions. Worked explanations show essential algebra and test a likely misconception. Condensing a long expression and using change of base are addressed in the next topic; this set concentrates on justified expansion and keeping the same mathematical meaning.