P2.5.2 - Laws of logarithms

Use log_a(xy) = log_a x + log_a y, log_a(x/y) = log_a x − log_a y, log_a(x^k) = k log_a x, log_a(1/x) = −log_a x and log_a a = 1, for valid positive arguments and a ≠ 1.

Use laws of logarithms to connect the rule to the data and decision in the question.

This matters because laws of logarithms determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply laws of logarithms to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Laws of logarithms is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.