P2.5 - Exponentials and logarithms

y = ax and its graph. a > 0, a ≠ 1.

Use y = ax and its graph to connect the rule to the data and decision in the question.

This matters because y = ax and its graph determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply y = ax and its graph to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: y = ax and its graph is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

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.

The solution of equations of the Students may use the change of base formula. form ax = b.

Use solving equations using logarithms to connect the rule to the data and decision in the question.

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

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

Boundary: use the formula and units given in the question, show the substitution and interpret the result; the calculation alone is not the conclusion.